A063425 -id:A063425 - cp's OEIS frontend

A096355 Number of unattainables <= 10^n, where unattainables are A063425.

Original entry on oeis.org

5, 44, 429, 4069, 39433, 388459, 3855173, 38374875, 382644491, 3819130611

Offset: 1

Jason Earls, Jun 30 2004

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

Cf. A063114.

a(9)-a(10) from Donovan Johnson, Jul 20 2010

A096922 Numbers n for which there is a unique k such that n = k + (product of nonzero digits of k).

Original entry on oeis.org

2, 4, 6, 8, 10, 11, 20, 23, 24, 28, 29, 32, 33, 34, 35, 41, 42, 45, 46, 47, 54, 56, 58, 60, 65, 67, 68, 70, 75, 77, 78, 81, 85, 89, 92, 94, 95, 99, 100, 101, 106, 107, 108, 109, 111, 124, 125, 128, 129, 130, 132, 133, 135, 140, 141, 143, 145, 146, 147, 152, 154, 156, 158

Offset: 1

Klaus Brockhaus, Jul 15 2004

			21 is the unique k such that k + (product of nonzero digits of k) = 23, hence 23 is a term.

%H P. A. Loomis, An Interesting Family of Iterated Sequences
%H P. A. Loomis, An Introduction to Digit Product Sequences, J. Rec. Math., 32 (2003-2004), 147-151.
%H P. A. Loomis, An Introduction to Digit Product Sequences, J. Rec. Math., 32 (2003-2004), 147-151. [Annotated archived copy]
%H Index entries for Colombian or self numbers and related sequences

Cf. A063114, A096347, A063425, A096922, A096923, A096924, A096925, A096926, A096927, A096928, A096929, A096930, A096931.

f[n_] := Block[{s = Sort[ IntegerDigits[n]]}, While[ s[[1]] == 0, s = Drop[s, 1]]; n + Times @@ s]; t = Table[0, {200}]; Do[ a = f[n]; If[a < 200, t[[a]]++ ], {n, 200}]; Select[ Range[ 200], t[[ # ]] == 1 &] (* Robert G. Wilson v, Jul 16 2004 *)

addpnd(n)=local(k,s,d);k=n;s=1;while(k>0,d=divrem(k,10);k=d[1];s=s*max(1,d[2]));n+s
{c=1;z=160;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,",")))}

A096347 Least number with n preimages (or immediate predecessors) under f(n) = n + (product of nonzero digits of n).

Original entry on oeis.org

1, 2, 12, 102, 116, 1098, 2072, 1014, 101134, 11014, 1011098, 1003525, 41021255, 210110985, 403130555, 481104655, 4401225555, 4811125555, 86413249555, 39011218055

Offset: 0

Jason Earls, Jun 29 2004

First occurrence of k in A096972.

a(20) > 10^11. [From Donovan Johnson, Nov 22 2009]

			a(3)=102 because 102 is the least number with three direct predecessors, 66: 66+6*6 = 102, 74: 74+7*4 = 102, 101: 101+1*1 = 102.

P. A. Loomis, An Introduction to Digit Product Sequences (see link).

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

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

a(8) to a(11) from Klaus Brockhaus, Jul 07 2004
a(12) from Robert G. Wilson v, Jul 15 2004
a(13)-a(19) from Donovan Johnson, Nov 22 2009

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}]

A230106 Number of m such that m + (product of nonzero digits of m) equals n.

Original entry on oeis.org

0, 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

Offset: 0

N. J. A. Sloane, Oct 13 2013

Number of times n appears in A063114.

Index entries for Colombian or self numbers and related sequences

Cf. A063108, A063114, A230099, A230104, A063425, A096922.

Variant of A096972.

# Maple code for A063114, A230106, A063425, A096922
with(LinearAlgebra):
read transforms; # to get digprod0
M:=1000;
lis1:=Array(0..M);
lis2:=Array(0..M);
ctmax:=4;
for i from 0 to ctmax do ct[i]:=Array(0..M); od:
for n from 0 to M do
m:=n+digprod0(n);
lis1[n]:=m;
if (m <= M) then lis2[m]:=lis2[m]+1; fi;
od:
t1:=[seq(lis1[i],i=0..M)]; # A063114
t2:=[seq(lis2[i],i=0..M)]; # A230106
COMPl(t1); # A063425
for i from 1 to M do h:=lis2[i];
if h <= ctmax then ct[h]:=[op(ct[h]),i]; fi; od:
len:=nops(ct[0]); [seq(ct[0][i],i=1..len)]; # A063425 again
len:=nops(ct[1]); [seq(ct[1][i],i=1..len)]; # A096922

a(1) corrected by Zak Seidov, Oct 24 2013

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

cp's OEIS Frontend

A096355 Number of unattainables <= 10^n, where unattainables are A063425.

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A096922 Numbers n for which there is a unique k such that n = k + (product of nonzero digits of k).

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A096347 Least number with n preimages (or immediate predecessors) under f(n) = n + (product of nonzero digits of n).

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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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A230106 Number of m such that m + (product of nonzero digits of m) equals n.

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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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