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Search: id:A063108
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| A063108 |
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a(1) = 1; a(n+1) = a(n) + product of nonzero digits of a(n). |
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+0
10
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
P. A. Loomis, An Interesting Family of Iterated Sequences
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FORMULA
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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.
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EXAMPLE
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a(2) = 1 + 1 = 2; a(3) = 4; a(6) = 16 + 1*6 = 22; a(22) = 206 + 2*6 = 218.
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MATHEMATICA
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f[ n_Integer ] := Block[{s = Sort[ IntegerDigits[ n ]]}, While[ s[[ 1 ]] == 0, s = Drop[ s, 1 ]]; n + Times @@ s]; NestList[ f, 1, 65 ]
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PROGRAM
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(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) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 18 2009]
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CROSSREFS
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Cf. A063112, A063113, A063114, A097050.
Sequence in context: A002081 A102039 A045844 this_sequence A161140 A058961 A130917
Adjacent sequences: A063105 A063106 A063107 this_sequence A063109 A063110 A063111
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KEYWORD
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base,easy,nonn,nice
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AUTHOR
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Paul A. Loomis (ploomis(AT)bloomu.edu), Aug 08 2001
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 09 2001
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