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Search: a133619 -id:a133619
Displaying 1-10 of 16 results found. page 1 2
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A133612 Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n satisfies 2^A(k) == A(k) (mod 10^k). +10
25
6, 3, 7, 8, 4, 9, 2, 3, 4, 3, 5, 3, 5, 7, 0, 5, 1, 6, 8, 9, 0, 8, 3, 3, 3, 5, 8, 9, 5, 1, 0, 0, 6, 2, 7, 8, 6, 9, 6, 8, 2, 5, 5, 4, 1, 0, 7, 5, 4, 2, 6, 8, 2, 6, 1, 4, 8, 2, 8, 2, 1, 2, 1, 2, 1, 9, 0, 7, 2, 9, 8, 3, 5, 5, 8, 9, 8, 9, 7, 1, 0, 4, 9, 0, 5, 2, 2, 0, 9, 1, 7, 8, 8, 8, 6, 5, 2, 2, 4, 4, 8, 3, 7, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
10-adic expansion of the iterated exponential 2^^n (A014221) for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 2^^n == 2948736 (mod 10^7).
Sequences A133612-A133619 and A144539-A144544 generalize the observation that 7^343 == 343 (mod 1000).
REFERENCES
M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011. ISBN 978-88-6178-789-6
Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..5999
J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), J. Int. Seq. 12 (2009) #09.8.8.
Robert G. Wilson v, Mathematica coding for "SuperPowerMod" and associated programs from Prof. Ian Vardi (Corrected Aug 24 2020)
EXAMPLE
63784923435357051689083335895100627869682554107542682614828212121907298... - Robert G. Wilson v, Feb 22 2014
2^36 = 68719476736 == 36 (mod 100), 2^736 == 736 (mod 1000), 2^8736 == 8736 (mod 10000), etc.
MATHEMATICA
(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[2, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Feb 22 2014 *)
CROSSREFS
Cf. A014221, A109405.
Cf. A133613, A133614, A133615, A133616, A133617, A133618, A133619, A144539, A144540, A144541, A144542, A144543, A144544.
KEYWORD
nonn,base
AUTHOR
Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007
EXTENSIONS
Edited by N. J. A. Sloane, Dec 22 2007 and Dec 22 2008
More terms from J. Luis A. Yebra, Dec 12 2008
a(68) onward from Robert G. Wilson v, Feb 22 2014
STATUS
approved
A133613 Decimal digits such that for all k >= 1, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n satisfies the congruence 3^A(k) == A(k) (mod 10^k). +10
18
7, 8, 3, 5, 9, 1, 4, 6, 4, 2, 6, 2, 7, 2, 6, 5, 7, 5, 4, 0, 1, 9, 5, 0, 9, 3, 4, 6, 8, 1, 5, 8, 4, 8, 1, 0, 7, 6, 9, 3, 2, 7, 8, 4, 3, 2, 2, 2, 3, 0, 0, 8, 3, 6, 6, 9, 4, 5, 0, 9, 7, 6, 9, 3, 9, 9, 8, 1, 6, 9, 9, 3, 6, 9, 7, 5, 3, 5, 2, 6, 5, 1, 5, 8, 3, 9, 1, 8, 1, 0, 5, 6, 2, 8, 4, 2, 4, 0, 4, 9, 8, 0, 5, 1, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
10-adic expansion of the iterated exponential 3^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n>9, 3^^n == 4195387 (mod 10^7).
This sequence also gives many final digits of Graham's number ...399618993967905496638003222348723967018485186439059104575627262464195387. - Paul Muljadi, Sep 08 2008 and J. Luis A. Yebra, Dec 22 2008
Graham's number can be represented as G(64):=3^^3^^...^^3 [see M. Gardner and Wikipedia], in which case its G(63) lowermost digits are guaranteed to match this sequence (i.e., the convergence speed of the base 3 is unitary - see A317905). To avoid such confusion, it would be best to interpret this sequence as a real-valued constant 0.783591464..., corresponding to 3^^k in the limit of k->infinity, and call it Graham's constant G(3). Generalizations to G(n) and G(n,base) are obvious. - Stanislav Sykora, Nov 07 2015
REFERENCES
M. Gardner, Mathematical Games, Scientific American 237, 18 - 28 (1977).
M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, p. 11-12, 69-78. ISBN 978-88-6178-789-6.
Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..10039
J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), J. Int. Seq. 12 (2009) #09.8.8.
Robert P. Munafo, Large Numbers [From Robert G. Wilson v, May 07 2010]
Reddit user atticdoor, Spotted an error in the comments of sequence A133613.
Marco Ripà, On the constant congruence speed of tetration, Notes on Number Theory and Discrete Mathematics, Volume 26, 2020, Number 3, Pages 245—260.
Marco Ripà, The congruence speed formula, Notes on Number Theory and Discrete Mathematics, 2021, 27(4), 43-61.
Wikipedia, Graham's number
FORMULA
a(n) = floor( A183613(n+1) / 10^n ).
EXAMPLE
783591464262726575401950934681584810769327843222300836694509769399816993697535...
Consider the sequence 3^^n: 1, 3, 27, 7625597484987, ... From 3^^3 = 7625597484987 onwards, all terms end with the digits 87. This follows from Euler's generalization of Fermat's little theorem.
MATHEMATICA
(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[3, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)
CROSSREFS
Cf. A133612, A133614, A133615, A133616, A133617, A133618, A133619, A144539, A144540, A144541, A144542, A144543, A144544, A317905, A318478.
KEYWORD
nonn,base
AUTHOR
Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007
EXTENSIONS
More terms from J. Luis A. Yebra, Dec 12 2008
Edited by N. J. A. Sloane, Dec 22 2008
More terms from Robert G. Wilson v, May 07 2010
STATUS
approved
A133614 Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n satisfies 4^A(k) == A(k) (mod 10^k). +10
17
6, 9, 8, 8, 2, 7, 1, 1, 4, 0, 9, 2, 5, 5, 5, 2, 0, 3, 2, 2, 6, 3, 9, 4, 9, 5, 3, 1, 4, 3, 9, 3, 1, 2, 0, 6, 5, 7, 5, 6, 3, 4, 2, 1, 3, 5, 2, 6, 0, 6, 2, 9, 5, 4, 0, 6, 6, 0, 7, 5, 9, 5, 6, 9, 0, 6, 1, 4, 6, 8, 8, 3, 8, 3, 6, 4, 8, 8, 0, 5, 2, 3, 0, 3, 2, 6, 2, 5, 4, 1, 1, 1, 9, 0, 9, 8, 0, 8, 1, 4, 3, 1, 0, 1, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
10-adic expansion of the iterated exponential 4^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 4^^n == 1728896 (mod 10^7).
REFERENCES
M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, p. 69-78. ISBN 978-88-6178-789-6.
Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..1024
J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), J. Int. Seq. 12 (2009) #09.8.8.
EXAMPLE
698827114092555203226394953143931206575634213526062954066075956906146883836488...
MATHEMATICA
(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[4, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)
CROSSREFS
Cf. A133612, A133613, A133615, A133616, A133617, A133618, A133619, A144539, A144540, A144541, A144542, A144543, A144544.
KEYWORD
nonn,base
AUTHOR
Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007
EXTENSIONS
More terms from J. Luis A. Yebra, Dec 12 2008
Edited by N. J. A. Sloane, Dec 22 2008
a(68) onward from Robert G. Wilson v, Mar 06 2014
STATUS
approved
A133615 Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n satisfies 5^A(k) == A(k) (mod 10^k). +10
17
5, 2, 1, 3, 0, 2, 8, 0, 4, 8, 1, 6, 2, 5, 1, 3, 9, 4, 7, 1, 1, 7, 8, 5, 3, 8, 0, 9, 5, 1, 1, 5, 6, 9, 8, 0, 4, 9, 2, 2, 9, 8, 9, 3, 3, 9, 8, 1, 3, 3, 1, 7, 7, 4, 6, 7, 1, 0, 2, 8, 3, 7, 5, 1, 7, 3, 1, 4, 1, 1, 9, 7, 8, 2, 9, 6, 2, 5, 5, 5, 3, 3, 0, 9, 0, 4, 7, 3, 1, 8, 5, 7, 4, 6, 9, 7, 2, 3, 0, 8, 9, 2, 6, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
10-adic expansion of the iterated exponential 5^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 5^^n == 8203125 (mod 10^7).
REFERENCES
M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, p. 69-78. ISBN 978-88-6178-789-6.
Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..1024
J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), J. Int. Seq. 12 (2009) #09.8.8.
EXAMPLE
521302804816251394711785380951156980492298933981331774671028375173141197829625...
MATHEMATICA
(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[5, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)
CROSSREFS
Cf. A133612, A133613, A133614, A133616, A133617, A133618, A133619, A144539, A144540, A144541, A144542, A144543, A144544.
KEYWORD
nonn,base
AUTHOR
Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007
EXTENSIONS
More terms from J. Luis A. Yebra, Dec 12 2008
Edited by N. J. A. Sloane, Dec 22 2008
a(68) onward from Robert G. Wilson v, Mar 06 2014
STATUS
approved
A133617 Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n satisfies 7^A(k) == A(k) (mod 10^k). +10
17
3, 4, 3, 2, 7, 1, 5, 6, 5, 1, 1, 5, 5, 6, 2, 1, 3, 3, 3, 4, 6, 3, 5, 8, 3, 3, 3, 7, 3, 6, 0, 8, 6, 0, 3, 6, 9, 5, 6, 7, 4, 1, 8, 2, 6, 6, 5, 9, 2, 6, 5, 3, 0, 8, 6, 5, 2, 8, 4, 4, 4, 7, 7, 7, 6, 7, 5, 4, 9, 1, 2, 9, 8, 6, 5, 7, 7, 0, 7, 8, 4, 2, 6, 3, 8, 5, 4, 8, 1, 9, 4, 5, 8, 3, 9, 9, 5, 4, 4, 0, 3, 8, 2, 2, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
10-adic expansion of the iterated exponential 7^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 7^^n == 5172343 (mod 10^7).
REFERENCES
M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, p. 69-78. ISBN 978-88-6178-789-6.
Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..1024
J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), J. Int. Seq. 12 (2009) #09.8.8.
EXAMPLE
343271565115562133346358333736086036956741826659265308652844477767549129865770...
Sequences A133612-A144544 generalize the observation that 7^343 == 343 (mod 1000).
MATHEMATICA
(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[7, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)
CROSSREFS
Cf. A133612, A133613, A133614, A133615, A133616, A133618, A133619, A144539, A144540, A144541, A144542, A144543, A144544.
KEYWORD
nonn,base
AUTHOR
Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007
EXTENSIONS
More terms from J. Luis A. Yebra, Dec 12 2008
Edited by N. J. A. Sloane, Dec 22 2008
a(68) onward from Robert G. Wilson v, Mar 06 2014
STATUS
approved
A133618 Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n satisfies 8^A(k) == A(k) (mod 10^k). +10
17
6, 5, 8, 5, 2, 2, 5, 9, 8, 6, 1, 4, 5, 3, 0, 7, 7, 5, 1, 2, 5, 1, 8, 0, 0, 1, 5, 8, 8, 5, 5, 9, 0, 2, 6, 1, 3, 9, 1, 1, 5, 6, 2, 9, 8, 3, 7, 7, 2, 0, 1, 5, 7, 3, 8, 8, 2, 6, 6, 7, 0, 3, 7, 5, 7, 2, 7, 4, 2, 4, 4, 2, 4, 3, 7, 5, 8, 4, 4, 2, 2, 1, 3, 0, 8, 8, 8, 8, 7, 1, 5, 9, 1, 2, 0, 1, 6, 0, 9, 8, 0, 5, 3, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
10-adic expansion of the iterated exponential 8^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 8^^n == 5225856 (mod 10^7).
REFERENCES
M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, p. 69-78. ISBN 978-88-6178-789-6.
Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..1024
J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), J. Int. Seq. 12 (2009) #09.8.8.
EXAMPLE
658522598614530775125180015885590261391156298377201573882667037572742442437584...
8^56 == 56 (mod 100), 8^856 == 856 (mod 1000), ...
MATHEMATICA
(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[8, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)
CROSSREFS
Cf. A133612, A133613, A133614, A133615, A133616, A133617, A133619, A144539, A144540, A144541, A144542, A144543, A144544.
KEYWORD
nonn,base
AUTHOR
Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007
EXTENSIONS
More terms from J. Luis A. Yebra, Dec 12 2008
Edited by N. J. A. Sloane, Dec 22 2008
a(68) onward from Robert G. Wilson v, Mar 06 2014
STATUS
approved
A133616 Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n satisfies 6^A(k) == A(k) (mod 10^k). +10
16
6, 5, 6, 8, 3, 2, 7, 4, 4, 7, 2, 2, 3, 9, 5, 5, 6, 9, 7, 6, 7, 3, 2, 1, 9, 6, 0, 1, 7, 5, 0, 6, 0, 5, 8, 6, 9, 1, 8, 0, 1, 3, 7, 9, 4, 6, 0, 4, 4, 7, 0, 4, 6, 4, 0, 2, 4, 6, 3, 7, 8, 1, 6, 7, 0, 8, 5, 0, 1, 4, 3, 4, 4, 4, 1, 8, 5, 7, 5, 9, 7, 0, 0, 4, 2, 9, 6, 3, 4, 1, 8, 9, 6, 0, 9, 8, 4, 5, 7, 0, 3, 5, 0, 8, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
10-adic expansion of the iterated exponential 6^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 6^^n == 7238656 (mod 10^7).
REFERENCES
M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, p. 69-78. ISBN 978-88-6178-789-6.
Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..1024
J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), J. Int. Seq. 12 (2009) #09.8.8.
EXAMPLE
656832744722395569767321960175060586918013794604470464024637816708501434441857...
MATHEMATICA
(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[6, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)
CROSSREFS
Cf. A133612, A133613, A133614, A133615, A133617, A133618, A133619, A144539, A144540, A144541, A144542, A144543, A144544.
KEYWORD
nonn,base
AUTHOR
Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007
EXTENSIONS
More terms from J. Luis A. Yebra, Dec 12 2008
Edited by N. J. A. Sloane, Dec 22 2008
a(68) onward from Robert G. Wilson v, Mar 06 2014
STATUS
approved
A144539 Unique sequence of digits a(0), a(1), a(2), .. such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1 } a(n)*10^n satisfies 11^A(k) == A(k) mod 10^k. +10
16
1, 1, 6, 6, 6, 6, 2, 7, 1, 9, 7, 8, 3, 0, 7, 6, 6, 2, 0, 2, 7, 1, 9, 8, 7, 9, 3, 4, 3, 2, 6, 9, 8, 1, 1, 7, 5, 1, 0, 2, 0, 4, 5, 9, 4, 3, 9, 9, 9, 4, 5, 3, 9, 3, 9, 2, 4, 3, 8, 4, 1, 6, 0, 5, 6, 8, 8, 0, 6, 4, 2, 9, 2, 6, 1, 6, 6, 4, 0, 9, 0, 3, 9, 4, 9, 6, 8, 9, 0, 8, 6, 9, 1, 8, 7, 5, 0, 5, 8, 6, 7, 4, 6, 5, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
REFERENCES
M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, p. 69-78. ISBN 978-88-6178-789-6.
Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..1024
J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), J. Int. Seq. 12 (2009) #09.8.8.
EXAMPLE
116666271978307662027198793432698117510204594399945393924384160568806429261664...
MATHEMATICA
(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[11, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)
CROSSREFS
Cf. A133612, A133613, A133614, A133615, A133616, A133617, A133618, A133619, A144540, A144541, A144542, A144543, A144544.
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Dec 20 2008
EXTENSIONS
a(68) onward from Robert G. Wilson v, Mar 06 2014
STATUS
approved
A144540 Unique sequence of digits a(0), a(1), a(2), .. such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1 } a(n)*10^n satisfies 12^A(k) == A(k) mod 10^k. +10
16
6, 1, 4, 2, 1, 0, 4, 5, 4, 1, 2, 4, 4, 1, 7, 1, 3, 9, 4, 8, 5, 8, 4, 8, 5, 3, 1, 9, 5, 3, 6, 9, 3, 2, 5, 7, 1, 9, 7, 7, 7, 8, 2, 3, 3, 9, 4, 2, 1, 0, 4, 8, 5, 7, 9, 6, 7, 9, 5, 6, 2, 5, 3, 5, 7, 6, 7, 5, 4, 1, 5, 0, 8, 2, 9, 0, 3, 6, 4, 1, 0, 7, 9, 6, 2, 8, 3, 8, 0, 3, 4, 4, 1, 4, 6, 4, 3, 9, 0, 4, 2, 3, 0, 5, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
REFERENCES
M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, p. 69-78. ISBN 978-88-6178-789-6.
Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..1024
J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), J. Int. Seq. 12 (2009) #09.8.8.
EXAMPLE
614210454124417139485848531953693257197778233942104857967956253576754150829036...
MATHEMATICA
(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[12, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)
CROSSREFS
Cf. A133612, A133613, A133614, A133615, A133616, A133617, A133618, A133619, A144539, A144541, A144542, A144543, A144544.
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Dec 20 2008
EXTENSIONS
a(68) onward from Robert G. Wilson v, Mar 06 2014
STATUS
approved
A144541 Unique sequence of digits a(0), a(1), a(2), .. such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1 } a(n)*10^n satisfies 13^A(k) == A(k) mod 10^k. +10
16
3, 5, 0, 5, 4, 0, 5, 5, 2, 8, 8, 4, 5, 9, 1, 8, 1, 2, 2, 4, 8, 8, 8, 7, 6, 9, 2, 0, 7, 1, 6, 8, 6, 9, 0, 4, 6, 7, 3, 2, 3, 5, 6, 8, 9, 4, 4, 3, 6, 6, 5, 6, 6, 3, 5, 9, 3, 1, 7, 0, 4, 3, 3, 7, 4, 6, 1, 4, 7, 6, 6, 9, 7, 2, 8, 5, 4, 7, 9, 3, 5, 5, 6, 7, 6, 5, 5, 8, 2, 1, 5, 0, 2, 2, 5, 4, 0, 5, 6, 8, 2, 7, 1, 8, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
REFERENCES
M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, p. 69-78. ISBN 978-88-6178-789-6.
Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..1024
J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), J. Int. Seq. 12 (2009) #09.8.8
EXAMPLE
350540552884591812248887692071686904673235689443665663593170433746147669728547...
MATHEMATICA
(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[13, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)
CROSSREFS
Cf. A133612, A133613, A133614, A133615, A133616, A133617, A133618, A133619, A144539, A144540, A144542, A144543, A144544.
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Dec 20 2008
EXTENSIONS
a(68) onward from Robert G. Wilson v, Mar 06 2014
STATUS
approved
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Last modified August 29 22:07 EDT 2024. Contains 375518 sequences. (Running on oeis4.)