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.

A063108 a(1) = 1; thereafter a(n+1) = a(n) + product of nonzero digits of a(n).

Original entry on oeis.org

1, 2, 4, 8, 16, 22, 26, 38, 62, 74, 102, 104, 108, 116, 122, 126, 138, 162, 174, 202, 206, 218, 234, 258, 338, 410, 414, 430, 442, 474, 586, 826, 922, 958, 1318, 1342, 1366, 1474, 1586, 1826, 1922, 1958, 2318, 2366, 2582, 2742, 2854, 3174, 3258, 3498, 4362
Offset: 1

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Author

Paul A. Loomis, Aug 08 2001

Keywords

Comments

Conjecture: no matter what the starting term is, the sequence eventually joins this one. This should be true in any base - base 2, for example, is trivial.
A063114 iterated, beginning with 1. - Reinhard Zumkeller, Jan 15 2012

Examples

			a(2) = 1 + 1 = 2; a(3) = 4; a(6) = 16 + 1*6 = 22; a(22) = 206 + 2*6 = 218.
		

Crossrefs

Programs

  • Haskell
    a063108_list = iterate a063114 1  -- Reinhard Zumkeller, Jan 15 2012
  • Maple
    with transforms;
    f:=proc(n) option remember; if n=1 then 1
    else f(n-1)+digprod(f(n-1)); fi; end;
    [seq(f(n),n=1..20)];
    # N. J. A. Sloane, Oct 12 2013
  • Mathematica
    f[ n_Integer ] := Block[{s = Sort[ IntegerDigits[ n ]]}, While[ s[[ 1 ]] == 0, s = Drop[ s, 1 ]]; n + Times @@ s]; NestList[ f, 1, 65 ]
    nxt[n_]:=n+Times@@Select[IntegerDigits[n],#>0&]; NestList[nxt,1,50] (* Harvey P. Dale, Oct 10 2012 *)
  • PARI
    lista(n)={ my(a=vector(n)); a[1]=1; for(i=1, #a-1, a[i+1] = a[i] + vecprod(select(x->x, digits(a[i])))); a } \\ Harry J. Smith, Aug 18 2009
    

Formula

A crude heuristic analysis suggests that a(n) grows roughly like (8/9 * (1-y))^(1/(1-y)) * n^(1/1-y) where y = log_10(4.5), i.e., that a(n) ~ 0.033591*n^2.8836.

Extensions

More terms from Robert G. Wilson v, Aug 09 2001