A063108 -id:A063108 - cp's OEIS frontend

A232486 a(1) = 3; thereafter a(n+1) = a(n) + product of nonzero digits of a(n).

3, 6, 12, 14, 18, 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, 4506

Offset: 1

N. J. A. Sloane, Nov 29 2013

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. A063018, A232485, A232487, A232488.

f:=proc(n) local t1,t2,i;
t1:=convert(n,base,10);
t2:=1;
for i from 1 to nops(t1) do if t1[i] <> 0 then t2:=t2*t1[i]; fi; od;
t2; end;
g:=n->n+f(n);
t1:=[3];
for n from 1 to 50 do t1:=[op(t1),g(t1[nops(t1)])]; od:
t1;

A232488 a(1) = 7; a(n+1) = a(n) + product of nonzero digits of a(n).

Original entry on oeis.org

7, 14, 18, 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, 4506, 4626, 4914

Offset: 1

N. J. A. Sloane, Nov 29 2013

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. A063108, A232486, A232488.

Maple
```
See A232486.
```

nxt[n_]:=n+Times@@Select[IntegerDigits[n],#!=0&]; NestList[nxt,7,50] (* Harvey P. Dale, Jun 13 2015 *)

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}]

A232487 a(1) = 5; a(n+1) = a(n) + product of nonzero digits of a(n).

Original entry on oeis.org

5, 10, 11, 12, 14, 18, 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

N. J. A. Sloane, Nov 29 2013

Harvey P. Dale, Table of n, a(n) for n = 1..1000
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. A063108, A232486, A232488.

Maple
```
See A232486.
```

NestList[#+Times@@Select[IntegerDigits[#],#>0&]&,5,50] (* Harvey P. Dale, Jul 07 2020 *)

A096729 Where records occur in A096287.

Original entry on oeis.org

1, 3, 5, 21, 37, 49, 51, 63, 4447, 5954, 6577, 9590, 12362, 38657, 42529, 42723, 154619, 158367, 512437, 965489, 978547, 1042723, 2377596, 2458779, 2687592, 2729784, 2976847, 2995687, 3233341, 3271507, 3378978, 3438666, 3447618

Offset: 1

Klaus Brockhaus and Jason Earls, Jul 06 2004

nonn

The records are given in A096728.

			A096287(21) = 10 is the fourth record, so A096729(4) = 21.

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. A096287, A063108.

a(23)-a(33) from Donovan Johnson, Nov 22 2009

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

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

A096728 Records in A096287.

Original entry on oeis.org

0, 5, 6, 10, 15, 16, 17, 322, 472, 474, 476, 487, 495, 894, 898, 900, 1437, 1443, 1456, 1459, 1460, 1461, 2594, 2653, 2661, 2674, 2899, 2900, 2905, 2907, 2908, 2915, 2919

Offset: 1

Klaus Brockhaus and Jason Earls, Jul 06 2004

Numbers n such that A096287(n) is a record are given in A096729.

			A096287(5) = 6 and A096287(k) < 6 for k < 5, hence 6 is a term.

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. A096287, A063108.

a(23)-a(33) from Donovan Johnson, Nov 22 2009

A248078 a(1) = 1; a(n+1) = a(n) + product of digits of a(n) + sum of digits of a(n).

Original entry on oeis.org

1, 3, 9, 27, 50, 55, 90, 99, 198, 288, 434, 493, 617, 673, 815, 869, 1324, 1358, 1495, 1694, 1930, 1943, 2068, 2084, 2098, 2117, 2142, 2167, 2267, 2452, 2545, 2761, 2861, 2974, 3500, 3508, 3524, 3658, 4400, 4408, 4424, 4566, 5307, 5322, 5394, 5955, 7104, 7116

Offset: 1

Gil Broussard, Sep 30 2014

Unlike A063108, this sequence includes in its formula the digit 0 in the product of digits of a(n).

			Given a(5)=50, then a(6)=50+(5+0)+(5*0)=55.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A063108, A004207.

f:= proc(x) local L;
  L:= convert(x,base,10);
  x + convert(L,`+`)+convert(L,`*`)
end proc:
A[1]:= 1:
for n from 2 to 100 do A[n]:= f(A[n-1]) od:
seq(A[i],i=1..100); # Robert Israel, Jun 25 2019

NestList[#+Total[IntegerDigits[#]]+Times@@IntegerDigits[#]&,1,50] (* Harvey P. Dale, Sep 11 2019 *)

lista(nn) = {prev = 1; print1(prev, ", "); for (n=1, nn, d = digits(prev); prev += sumdigits(prev) + prod(k=1, #d, d[k]); print1(prev, ", "););} \\ Michel Marcus, Oct 01 2014

A273913 Consider the sequence b(k) with initial values b(1) = 1 and b(2) = n and satisfying b(k) = b(k-1) + Pd(b(k-2)), where Pd(x) is the product of the digits of x. Then b(k) eventually becomes constant, and this constant is a(n).

Original entry on oeis.org

1902, 1902, 730, 230, 550, 420, 502, 1902, 2150, 1074, 1074, 1074, 1902, 1902, 8170, 730, 550, 730, 600, 230, 80, 230, 470, 550, 1074, 4045, 4990, 180, 230, 106, 90, 4990, 1062, 102, 902, 1230, 730, 108, 1406, 1017, 1410, 630, 2038, 505, 230, 1810, 150, 2306, 630

Offset: 1

Paolo P. Lava, Jun 17 2016

Maximum value in the first 10^5 terms is a(6874) = 209875, from b(128) on.

First n's whose last repetitive number of the sequence b(k) is a multiple: 1, 2, 5, 6, 34, 42, 135, 195, 460, 893, 2370, 4230, 7165, 237945.

			b(1) = 1, b(2) = 7. Then:
b(3) = 7 + Pd(1) = 7+1 = 8; b(4) = 8 + Pd(7) = 8+7 = 15;
b(5) = 15 + Pd(8) = 15+8 = 23; b(6) = 23 + Pd(15) = 23+5 = 28;
b(7) = 28 + Pd(23) = 28+6 = 34; b(8) = 34 + Pd(28) = 34+16 = 50;
…
b(19) = 270 + Pd(214) = 270+8 = 278; b(20) = 278 + Pd(270) = 278+0 = 278;
b(21) = 278 + Pd(278) = 278+112 = 390; b(22) = 390 + Pd(278) = 390+112 = 502;
b(23) = 502 + Pd(502) = 502+0 = 502; therefore a(7) = 502.

Paolo P. Lava, Table of n, a(n) for n = 1..10000

Cf. A007954, A063108.

with(numtheory); T:=proc(w) local x, y, z; x:=w; y:=1;
for z from 1 to ilog10(x)+1 do y:=y*(x mod 10); x:=trunc(x/10); od; y; end:
P:=proc(q) local a1,a2,a3,n; for n from 1 to q do a1:=1; a2:=n; a3:=T(a1)+a2;
while not (a1=a2 and a2=a3) do a1:=a2; a2:=a3; a3:=T(a1)+a2; od;  print(a1);
od; end: P(10^7);

a[n_] := Block[{b=0, c=1, d=n, p}, While[! (b == c == d), b=c; p = Times @@ IntegerDigits@ c; c = d; d += p]; d]; Array[a, 50] (* Giovanni Resta, Jun 20 2016 *)

pd(n) = my(d=digits(n)); prod(k=1, #d, d[k]);
a(n) = {ba = 1; bb = n; bc = bb + pd(ba); while (!((ba ==bb) && (bc == bb)), newb = bb + pd(ba); ba = bb; bb = bc; bc = bb + pd(ba);); bc;} \\ Michel Marcus, Jun 20 2016

cp's OEIS Frontend

A232486 a(1) = 3; thereafter a(n+1) = a(n) + product of nonzero digits of a(n).

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Maple

A232488 a(1) = 7; a(n+1) = a(n) + product of nonzero digits of a(n).

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Programs

Maple

Mathematica

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

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Programs

Mathematica

A232487 a(1) = 5; a(n+1) = a(n) + product of nonzero digits of a(n).

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Programs

Maple

Mathematica

A096729 Where records occur in A096287.

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

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Maple

Extensions

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

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A096728 Records in A096287.

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A248078 a(1) = 1; a(n+1) = a(n) + product of digits of a(n) + sum of digits of a(n).

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Maple