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Search: a047901 -id:a047901
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A057147
a(n) = n times sum of digits of n.
+10
25
0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 10, 22, 36, 52, 70, 90, 112, 136, 162, 190, 40, 63, 88, 115, 144, 175, 208, 243, 280, 319, 90, 124, 160, 198, 238, 280, 324, 370, 418, 468, 160, 205, 252, 301, 352, 405, 460, 517, 576, 637, 250, 306, 364, 424, 486, 550, 616
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
A056992(n) = A010888(a(n)). - Reinhard Zumkeller, Mar 19 2014
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
F. B. Diniz, About a new family of sequences, arXiv:1607.06082 [math.GM], 2016.
FORMULA
a(n) = n*A007953(n). - Michel Marcus, Aug 10 2014
G.f.: x * (d/dx) (1/(1 - x))*Sum_{k>=1} (x^k - x^(10^k+k) - 9*x^(10^k))/(1 - x^(10^k)). - Ilya Gutkovskiy, Mar 27 2018
MAPLE
for n from 0 to 150 do printf(`%d, `, n*add(convert(n, base, 10)[i], i=1..nops(convert(n, base, 10)))) od:
MATHEMATICA
Table[n*Total[IntegerDigits[n]], {n, 0, 100}]
PROG
(Haskell)
a057147 n = a007953 n * n -- Reinhard Zumkeller, Mar 19 2014
(PARI) a(n) = n*sumdigits(n) \\ Franklin T. Adams-Watters, Aug 03 2014
(Python)
[n*sum([int(d) for d in str(n)]) for n in range(10**5)] # Chai Wah Wu, Aug 05 2014
CROSSREFS
Cf. A007953, A003634, A005349, A052489, A052490, A003635, A245788.
Iterations: A047892 (start=2), A047912 (start=3), A047897 (start=5), A047898 (start=6), A047899 (start=7), A047900 (start=8), A047901 (start=9), A047902 (start=11).
KEYWORD
nonn,base,easy,look
AUTHOR
N. J. A. Sloane, Sep 13 2000
EXTENSIONS
More terms from James A. Sellers and Larry Reeves (larryr(AT)acm.org), Sep 13 2000
STATUS
approved
A047892
a(1) = 2; for n > 0, a(n+1) = a(n) * sum of digits of a(n).
+10
15
2, 4, 16, 112, 448, 7168, 157696, 5361664, 166211584, 5651193856, 276908498944, 19383594926080, 1298700860047360, 79220752462888960, 6733763959345561600, 592571228422409420800, 45035413360103115980800
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(n) mod 9 = A010712(n-1) for n > 1. - Reinhard Zumkeller, Sep 23 2007
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..250
FORMULA
a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014
MATHEMATICA
NestList[# Total[IntegerDigits[#]]&, 2, 20] (* Harvey P. Dale, Jul 18 2011 *)
PROG
(Haskell)
a047892 n = a047892_list !! (n-1)
a047892_list = iterate a057147 2 -- Reinhard Zumkeller, Mar 19 2014
CROSSREFS
Cf. A004207.
Cf. A007953.
Cf. A047912 (start=3), A047897 (start=5), A047898 (start=6), A047899 (start=7), A047900 (start=8), A047901 (start=9), A047902 (start=11).
KEYWORD
nonn,base,easy,nice
AUTHOR
Miklos SZABO (mike(AT)ludens.elte.hu)
EXTENSIONS
Offset changed by Reinhard Zumkeller, Mar 19 2014
STATUS
approved
A047897
a(1) = 5; for n > 0, a(n+1) = a(n) * sum of digits of a(n).
+10
11
5, 25, 175, 2275, 36400, 473200, 7571200, 166566400, 5663257600, 226530304000, 5663257600000, 226530304000000, 5663257600000000, 226530304000000000, 5663257600000000000, 226530304000000000000, 5663257600000000000000
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
After a(9), every second element has the same beginning. a(11+2k) = 40 * a(10+2k) = 40 * 25 * a(9+2k).
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..250
FORMULA
a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014
MATHEMATICA
NestList[#*Total[IntegerDigits[#]]&, 5, 20] (* Harvey P. Dale, Jan 25 2014 *)
PROG
(Haskell)
a047897 n = a047897_list !! (n-1)
a047897_list = iterate a057147 5 -- Reinhard Zumkeller, Mar 19 2014
CROSSREFS
Cf. A047892 (start=2), A047912 (start=3), A047898 (start=6), A047899 (start=7), A047900 (start=8), A047901 (start=9), A047902 (start=11).
KEYWORD
easy,nonn,base
AUTHOR
Miklos SZABO (mike(AT)ludens.elte.hu)
STATUS
approved
A047900
a(1) = 8; for n > 0, a(n+1) = a(n) * sum of digits of a(n).
+10
11
8, 64, 640, 6400, 64000, 640000, 6400000, 64000000, 640000000, 6400000000, 64000000000, 640000000000, 6400000000000, 64000000000000, 640000000000000, 6400000000000000, 64000000000000000, 640000000000000000
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
After the 2nd element, every element has the same beginning.
a(3+k) = 10 * a(2+k).
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..250
FORMULA
a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014
MATHEMATICA
NestList[# Total[IntegerDigits[#]]&, 8, 20] (* or *) Join[{8}, NestList[ 10#&, 64, 20]] (* Harvey P. Dale, Jul 03 2020 *)
PROG
(Haskell)
a047900 n = a047900_list !! (n-1)
a047900_list = iterate a057147 8 -- Reinhard Zumkeller, Mar 19 2014
CROSSREFS
Cf. A047892 (start=2), A047912 (start=3), A047897 (start=5), A047898 (start=6), A047899 (start=7), A047901 (start=9), A047902 (start=11).
KEYWORD
easy,nonn,base
AUTHOR
Miklos SZABO (mike(AT)ludens.elte.hu)
STATUS
approved
A047902
a(1) = 11; for n > 0, a(n+1) = a(n) * sum of digits of a(n).
+10
11
11, 22, 88, 1408, 18304, 292864, 9078784, 390387712, 15615508480, 671466864640, 38945078149120, 2375649767096320, 180549382299320320, 12638456760952422400, 960522713832384102400, 67236589968266887168000
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..250
FORMULA
a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014
PROG
(Haskell)
a047902 n = a047902_list !! (n-1)
a047902_list = iterate a057147 11 -- Reinhard Zumkeller, Mar 19 2014
CROSSREFS
Cf. A047892 (start=2), A047912 (start=3), A047897 (start=5), A047898 (start=6), A047899 (start=7), A047900 (start=8), A047901 (start=9).
KEYWORD
easy,nonn,base
AUTHOR
Miklos SZABO (mike(AT)ludens.elte.hu)
STATUS
approved
A047898
a(1) = 6; for n > 0, a(n+1) = a(n) * (sum of digits of a(n)).
+10
10
6, 36, 324, 2916, 52488, 1417176, 38263752, 1377495072, 61987278240, 3347313024960, 150629086123200, 6778308875544000, 488038239039168000, 35138753210820096000, 2213741452281666048000, 159389384564279955456000
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..250
FORMULA
a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014
MATHEMATICA
Nest[Append[#, # Total@ IntegerDigits@ # &@ Last[#]] &, {6}, 15] (* Michael De Vlieger, Jul 08 2019 *)
PROG
(Haskell)
a047898 n = a047898_list !! (n-1)
a047898_list = iterate a057147 6 -- Reinhard Zumkeller, Mar 19 2014
(Python)
A047898_list, l = [6], 6
for _ in range(10**2):
....l *= sum(int(d) for d in str(l))
....A047898_list.append(l) # Chai Wah Wu, Jan 04 2015
CROSSREFS
Cf. A047892 (start=2), A047912 (start=3), A047897 (start=5), A047899 (start=7), A047900 (start=8), A047901 (start=9), A047902 (start=11).
KEYWORD
easy,nonn,base
AUTHOR
Miklos SZABO (mike(AT)ludens.elte.hu)
STATUS
approved
A047899
a(1) = 7; for n > 0, a(n+1) = a(n) * sum of digits of a(n).
+10
10
7, 49, 637, 10192, 132496, 3312400, 43061200, 688979200, 33759980800, 1755519001600, 70220760064000, 2387505842176000, 138475338846208000, 9693273719234560000, 736688802661826560000, 64828614634240737280000
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..250
FORMULA
a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014
PROG
(Haskell)
a047899 n = a047899_list !! (n-1)
a047899_list = iterate a057147 7 -- Reinhard Zumkeller, Mar 19 2014
CROSSREFS
Cf. A047892 (start=2), A047912 (start=3), A047897 (start=5), A047898 (start=6), A047900 (start=8), A047901 (start=9), A047902 (start=11).
KEYWORD
nonn,base,easy
AUTHOR
Miklos SZABO (mike(AT)ludens.elte.hu)
STATUS
approved
A047912
a(1) = 3; for n > 0, a(n+1) = a(n) * sum of digits of a(n).
+10
10
3, 9, 81, 729, 13122, 118098, 3188646, 114791256, 4132485216, 148769467776, 10711401679872, 578415690713088, 41645929731342336, 2998506940656648192, 296852187125008171008, 24045027157125661851648
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Apart from the first term, the same as A047901. - R. J. Mathar, Oct 18 2008
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..250
FORMULA
a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014
MATHEMATICA
NestList[# Total[IntegerDigits[#]]&, 3, 20] (* Harvey P. Dale, Mar 21 2011 *)
PROG
(Haskell)
a047912 n = a047912_list !! (n-1)
a047912_list = iterate a057147 3 -- Reinhard Zumkeller, Mar 19 2014
CROSSREFS
Cf. A047892 (start=2), A047897 (start=5), A047898 (start=6), A047899 (start=7), A047900 (start=8), A047901 (start=9), A047902 (start=11).
KEYWORD
easy,nice,nonn,base
AUTHOR
Miklos SZABO (mike(AT)ludens.elte.hu)
STATUS
approved
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