A063108 a(1) = 1; thereafter a(n+1) = a(n) + product of nonzero digits of a(n).
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
Examples
a(2) = 1 + 1 = 2; a(3) = 4; a(6) = 16 + 1*6 = 22; a(22) = 206 + 2*6 = 218.
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000
- P. A. Loomis, An Interesting Family of Iterated Sequences
- P. A. Loomis, An Introduction to Digit Product Sequences, J. Rec. Math., 32 (2003-2004), 147-151.
- P. A. Loomis, An Introduction to Digit Product Sequences, J. Rec. Math., 32 (2003-2004), 147-151. [Annotated archived copy]
- Index entries for Colombian or self numbers and related sequences
Crossrefs
Programs
-
Haskell
a063108_list = iterate a063114 1 -- Reinhard Zumkeller, Jan 15 2012
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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
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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
Comments