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A133619
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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 9^A(k) == A(k) (mod 10^k).
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17
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9, 8, 2, 5, 4, 7, 2, 9, 3, 7, 9, 5, 7, 8, 0, 8, 4, 7, 0, 1, 6, 5, 7, 4, 3, 0, 5, 6, 2, 7, 2, 8, 4, 5, 2, 5, 7, 0, 0, 5, 8, 9, 9, 8, 8, 7, 4, 0, 4, 1, 9, 4, 9, 8, 8, 6, 8, 4, 6, 8, 1, 9, 9, 2, 6, 2, 0, 1, 3, 7, 5, 4, 1, 6, 1, 3, 6, 0, 7, 3, 8, 5, 8, 4, 6, 0, 0, 2, 0, 6, 3, 2, 5, 3, 7, 6, 7, 2, 9, 5, 7, 4, 3, 2, 4
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OFFSET
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0,1
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COMMENTS
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10-adic expansion of the iterated exponential 9^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 9^^n == 2745289 (mod 10^7).
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REFERENCES
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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.
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LINKS
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EXAMPLE
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982547293795780847016574305627284525700589988740419498868468199262013754161360...
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MATHEMATICA
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(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[9, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)
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CROSSREFS
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Cf. A133612, A133613, A133614, A133615, A133616, A133617, A133618, A144539, A144540, A144541, A144542, A144543, A144544.
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KEYWORD
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nonn,base
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AUTHOR
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Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007
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EXTENSIONS
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More terms from J. Luis A. Yebra, Dec 12 2008
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STATUS
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approved
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