A096347 -id:A096347 - cp's OEIS frontend

A096930 Numbers n for which there are exactly nine k such that n = k + (product of nonzero digits of k).

11014, 100774, 111014, 412055, 510142, 511146, 633296, 931395, 983025, 1008305, 1011125, 1031414, 1100774, 1101642, 1108305, 1111014, 1412055, 1510142, 1511146, 1633296, 1931395, 1983025, 2011125, 2011305, 2012725, 2110145

Offset: 1

Klaus Brockhaus, Jul 15 2004

			88486, 96454, 99073, 99154, 99316, 100594, 100654, 100718 and 100732 are the only nine k such that k + (product of nonzero digits of k) = 100774, hence 100774 is a term.

Cf. A063114, A096347, A096922 - A096929, A096931.

Select[Tally[Table[n+Times@@DeleteCases[IntegerDigits[n],0],{n, 2111000}]],#[[2]]==9&][[All,1]]//Sort (* Harvey P. Dale, Sep 15 2019 *)

{c=9;z=2120000;v=vector(z);for(n=1,z+1,k=addpnd(n);if(k<=z,v[k]=v[k]+1));for(j=1,length(v),if(v[j]==c,print1(j,",")))} \\for function addpnd see A096922

A096972 Number of preimages of n (or immediate predecessors) under map f(k) = k + (product of nonzero digits of k).

Original entry on oeis.org

0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 1, 1, 0, 2, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 2, 1, 0, 1, 0, 1, 0, 2, 0, 0, 1, 2, 1, 1, 0, 1, 0, 0, 0, 2, 1, 0, 1, 1, 0, 2, 1, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 1, 1, 3, 0, 2, 0

Offset: 1

Robert G. Wilson v, Jul 16 2004

Index entries for Colombian or self numbers and related sequences

Cf. A063108, A096347, A063425, A096922, A096923, A096924, A096925, A096926, A096927, A096928, A096929, A096930, A096931, A230106 (a variant).

f[n_] := Block[{s = Sort[ IntegerDigits[ n]]}, While[ s[[1]] == 0, s = Drop[s, 1]]; n + Times @@ s]; t = Table[0, {111}]; Do[ t[[f [n]]]++, {n, 111}]; Table[ t[[n]], {n, 105}]

A095992 a(1) = 30; for n > 1, a(n+1) = a(n) + {product of nonzero digits of a(n)}.

Original entry on oeis.org

30, 33, 42, 50, 55, 80, 88, 152, 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, 4506, 4626, 4914, 5058, 5258, 5658

Offset: 1

Julien Piquet (julipiquet(AT)yahoo.fr), Jul 18 2004

From a puzzle; explanation found by Pierre Roger.

Frank Rubin, Number Series

Cf. A063108, A096347, A096972, A063108, A063425, A096922, A096923, A096924, A096925, A096926, A096927, A096928, A096929, A096930, A096931, A096973, A096987.

a[1] = 30; a[n_] := a[n] = Block[{s = Sort[ IntegerDigits[a[n - 1]]]}, While[ s[[1]] == 0, s = Drop[s, 1]]; a[n - 1] + Times @@ s]; Table[ a[n], {n, 50}]
nxt[n_] := n+Times@@Select[IntegerDigits[n], #>0&]; NestList[nxt,30,50] (* Harvey P. Dale, Jan 08 2011 *)

The proposer suggests that this web site may contain other sequences also.

Edited and extended by Robert G. Wilson v and Klaus Brockhaus, Jul 20 2004

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A096930 Numbers n for which there are exactly nine k such that n = k + (product of nonzero digits of k).

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A096972 Number of preimages of n (or immediate predecessors) under map f(k) = k + (product of nonzero digits of k).

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A095992 a(1) = 30; for n > 1, a(n+1) = a(n) + {product of nonzero digits of a(n)}.

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