cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A057147 a(n) = n times sum of digits of n.

Original entry on oeis.org

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
Offset: 0

Views

Author

N. J. A. Sloane, Sep 13 2000

Keywords

Comments

A056992(n) = A010888(a(n)). - Reinhard Zumkeller, Mar 19 2014

Links

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).

Programs

  • Haskell
    a057147 n = a007953 n * n  -- Reinhard Zumkeller, Mar 19 2014
  • 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}]
  • 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

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

Extensions

More terms from James Sellers and Larry Reeves (larryr(AT)acm.org), Sep 13 2000

A047892 a(1) = 2; for n > 0, a(n+1) = a(n) * sum of digits of a(n).

Original entry on oeis.org

2, 4, 16, 112, 448, 7168, 157696, 5361664, 166211584, 5651193856, 276908498944, 19383594926080, 1298700860047360, 79220752462888960, 6733763959345561600, 592571228422409420800, 45035413360103115980800
Offset: 1

Views

Author

Miklos SZABO (mike(AT)ludens.elte.hu)

Keywords

Comments

a(n) mod 9 = A010712(n-1) for n > 1. - Reinhard Zumkeller, Sep 23 2007

Links

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).

Programs

  • Haskell
    a047892 n = a047892_list !! (n-1)
a047892_list = iterate a057147 2  -- Reinhard Zumkeller, Mar 19 2014
  • Mathematica
    NestList[# Total[IntegerDigits[#]]&,2,20] (* Harvey P. Dale, Jul 18 2011 *)

Formula

a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014

Extensions

Offset changed by Reinhard Zumkeller, Mar 19 2014

A047897 a(1) = 5; for n > 0, a(n+1) = a(n) * sum of digits of a(n).

Original entry on oeis.org

5, 25, 175, 2275, 36400, 473200, 7571200, 166566400, 5663257600, 226530304000, 5663257600000, 226530304000000, 5663257600000000, 226530304000000000, 5663257600000000000, 226530304000000000000, 5663257600000000000000
Offset: 1

Views

Author

Miklos SZABO (mike(AT)ludens.elte.hu)

Keywords

Comments

After a(9), every second element has the same beginning. a(11+2k) = 40 * a(10+2k) = 40 * 25 * a(9+2k).

Links

Crossrefs

Cf. A047892 (start=2), A047912 (start=3), A047898 (start=6), A047899 (start=7), A047900 (start=8), A047901 (start=9), A047902 (start=11).

Programs

  • Haskell
    a047897 n = a047897_list !! (n-1)
a047897_list = iterate a057147 5  -- Reinhard Zumkeller, Mar 19 2014
  • Mathematica
    NestList[#*Total[IntegerDigits[#]]&,5,20] (* Harvey P. Dale, Jan 25 2014 *)

Formula

a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014

A047900 a(1) = 8; for n > 0, a(n+1) = a(n) * sum of digits of a(n).

Original entry on oeis.org

8, 64, 640, 6400, 64000, 640000, 6400000, 64000000, 640000000, 6400000000, 64000000000, 640000000000, 6400000000000, 64000000000000, 640000000000000, 6400000000000000, 64000000000000000, 640000000000000000
Offset: 1

Views

Author

Miklos SZABO (mike(AT)ludens.elte.hu)

Keywords

Comments

After the 2nd element, every element has the same beginning.
a(3+k) = 10 * a(2+k).

Links

Crossrefs

Cf. A047892 (start=2), A047912 (start=3), A047897 (start=5), A047898 (start=6), A047899 (start=7), A047901 (start=9), A047902 (start=11).

Programs

  • Haskell
    a047900 n = a047900_list !! (n-1)
a047900_list = iterate a057147 8  -- Reinhard Zumkeller, Mar 19 2014
  • Mathematica
    NestList[# Total[IntegerDigits[#]]&,8,20] (* or *) Join[{8},NestList[ 10#&,64,20]] (* Harvey P. Dale, Jul 03 2020 *)

Formula

a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014

A047902 a(1) = 11; for n > 0, a(n+1) = a(n) * sum of digits of a(n).

Original entry on oeis.org

11, 22, 88, 1408, 18304, 292864, 9078784, 390387712, 15615508480, 671466864640, 38945078149120, 2375649767096320, 180549382299320320, 12638456760952422400, 960522713832384102400, 67236589968266887168000
Offset: 1

Views

Author

Miklos SZABO (mike(AT)ludens.elte.hu)

Keywords

Links

Crossrefs

Cf. A047892 (start=2), A047912 (start=3), A047897 (start=5), A047898 (start=6), A047899 (start=7), A047900 (start=8), A047901 (start=9).

Programs

  • Haskell
    a047902 n = a047902_list !! (n-1)
a047902_list = iterate a057147 11  -- Reinhard Zumkeller, Mar 19 2014

Formula

a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014

A047898 a(1) = 6; for n > 0, a(n+1) = a(n) * (sum of digits of a(n)).

Original entry on oeis.org

6, 36, 324, 2916, 52488, 1417176, 38263752, 1377495072, 61987278240, 3347313024960, 150629086123200, 6778308875544000, 488038239039168000, 35138753210820096000, 2213741452281666048000, 159389384564279955456000
Offset: 1

Views

Author

Miklos SZABO (mike(AT)ludens.elte.hu)

Keywords

Links

Crossrefs

Cf. A047892 (start=2), A047912 (start=3), A047897 (start=5), A047899 (start=7), A047900 (start=8), A047901 (start=9), A047902 (start=11).

Programs

  • Haskell
    a047898 n = a047898_list !! (n-1)
a047898_list = iterate a057147 6  -- Reinhard Zumkeller, Mar 19 2014
  • Mathematica
    Nest[Append[#, # Total@ IntegerDigits@ # &@ Last[#]] &, {6}, 15] (* Michael De Vlieger, Jul 08 2019 *)
  • 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

Formula

a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014

A047899 a(1) = 7; for n > 0, a(n+1) = a(n) * sum of digits of a(n).

Original entry on oeis.org

7, 49, 637, 10192, 132496, 3312400, 43061200, 688979200, 33759980800, 1755519001600, 70220760064000, 2387505842176000, 138475338846208000, 9693273719234560000, 736688802661826560000, 64828614634240737280000
Offset: 1

Views

Author

Miklos SZABO (mike(AT)ludens.elte.hu)

Keywords

Links

Crossrefs

Cf. A047892 (start=2), A047912 (start=3), A047897 (start=5), A047898 (start=6), A047900 (start=8), A047901 (start=9), A047902 (start=11).

Programs

  • Haskell
    a047899 n = a047899_list !! (n-1)
a047899_list = iterate a057147 7  -- Reinhard Zumkeller, Mar 19 2014

Formula

a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014

A047901 a(1) = 9; a(n+1) = a(n) * sum of decimal digits of a(n).

Original entry on oeis.org

9, 81, 729, 13122, 118098, 3188646, 114791256, 4132485216, 148769467776, 10711401679872, 578415690713088, 41645929731342336, 2998506940656648192, 296852187125008171008, 24045027157125661851648, 2164052444141309566648320
Offset: 1

Views

Author

Miklos SZABO (mike(AT)ludens.elte.hu)

Keywords

Links

Crossrefs

Cf. A047892 (start=2), A047912 (start=3), A047897 (start=5), A047898 (start=6), A047899 (start=7), A047900 (start=8), A047902 (start=11).

Programs

  • Haskell
    a047901 n = a047901_list !! (n-1)
a047901_list = iterate a057147 9  -- Reinhard Zumkeller, Mar 19 2014
  • Mathematica
    NestList[# Total[IntegerDigits[#]]&,9,20] (* Harvey P. Dale, Feb 07 2022 *)
  • Python
    A047901_list, l = [9], 9
for _ in range(10**2):
    l *= sum(int(d) for d in str(l))
    A047901_list.append(l) # Chai Wah Wu, Jan 04 2015

Formula

a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010

A135207 a(n)=Sum_digits{n^Sum_digits[a(n-1)]}, with a(0)=1.

Original entry on oeis.org

1, 1, 2, 9, 19, 40, 18, 28, 37, 45, 1, 2, 9, 46, 67, 81, 64, 55, 54, 73, 7, 36, 55, 49, 99, 109, 64, 63, 64, 34, 18, 55, 76, 81, 73, 73, 72, 82, 79, 90, 19, 49, 99, 136, 82, 63, 64, 70, 54, 73, 40, 27, 82, 82, 72, 82, 70, 72, 91, 49, 36, 64, 91, 99, 145, 79, 126, 82, 58, 126, 28
Offset: 0

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Dec 03 2007

Keywords

Links

Crossrefs

Cf. A047912, A066588, A108827.

Programs

  • Maple
    P:=proc(n) local a,i,k,w; a:=1; print(a); for i from 1 by 1 to n do w:=0; k:=a; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; k:=i^w; w:=0; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; a:=w; print(w); od; end: P(100);
  • Mathematica
    nxt[{n_,a_}]:={n+1,Total[IntegerDigits[(n+1)^Total[IntegerDigits[a]]]]}; NestList[nxt,{0,1},70][[;;,2]] (* Harvey P. Dale, Nov 03 2024 *)
Showing 1-9 of 9 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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