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 A063108 a(1) = 1; a(n+1) = a(n) + product of nonzero digits of a(n). 22
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 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] 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. EXAMPLE a(2) = 1 + 1 = 2; a(3) = 4; a(6) = 16 + 1*6 = 22; a(22) = 206 + 2*6 = 218. 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 *) PROG (PARI) ProdNzD(x)= { p=1; while (x>9, d=x-10*(x\10); if (d, p*=d); x\=10); return(p*x) } { for (n=1, 10000, if (n>1, a+=ProdNzD(a), a=1); write("b063108.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 18 2009 (Haskell) a063108_list = iterate a063114 1  -- Reinhard Zumkeller, Jan 15 2012 CROSSREFS Cf. A063112, A063113, A063114, A097050, A051801, A096355, A230102, A232485, A232486, A232487, A232488. Sequence in context: A045844 A254062 A230102 * A161140 A257350 A257165 Adjacent sequences:  A063105 A063106 A063107 * A063109 A063110 A063111 KEYWORD base,easy,nonn,nice,look AUTHOR Paul A. Loomis, Aug 08 2001 EXTENSIONS More terms from Robert G. Wilson v, Aug 09 2001 STATUS approved

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Last modified October 16 23:45 EDT 2019. Contains 328103 sequences. (Running on oeis4.)