A063112 -id:A063112 - cp's OEIS frontend

A063108 a(1) = 1; thereafter a(n+1) = a(n) + product of nonzero digits of a(n).

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

Offset: 1

Paul A. Loomis, Aug 08 2001

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

			a(2) = 1 + 1 = 2; a(3) = 4; a(6) = 16 + 1*6 = 22; a(22) = 206 + 2*6 = 218.

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]
Index entries for Colombian or self numbers and related sequences

Cf. A063112, A063113, A063114, A097050, A051801, A096355, A230102, A232485, A232486, A232487, A232488.

a063108_list = iterate a063114 1  -- Reinhard Zumkeller, Jan 15 2012

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

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 *)

lista(n)={ my(a=vector(n)); a[1]=1; for(i=1, #a-1, a[i+1] = a[i] + vecprod(select(x->x, digits(a[i])))); a } \\ Harry J. Smith, Aug 18 2009

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.

More terms from Robert G. Wilson v, Aug 09 2001

A063114 a(n) = n + product of the nonzero digits of n.

Original entry on oeis.org

2, 4, 6, 8, 10, 12, 14, 16, 18, 11, 12, 14, 16, 18, 20, 22, 24, 26, 28, 22, 23, 26, 29, 32, 35, 38, 41, 44, 47, 33, 34, 38, 42, 46, 50, 54, 58, 62, 66, 44, 45, 50, 55, 60, 65, 70, 75, 80, 85, 55, 56, 62, 68, 74, 80, 86, 92, 98, 104, 66, 67, 74, 81, 88, 95, 102, 109, 116

Offset: 1

N. J. A. Sloane, Aug 08 2001

			a(59) = 59 + 5*9 = 104. a(66) = 66 + 6*6 = 102.

Harry J. Smith, Table of n, a(n) for n = 1..1000
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. A051801, A063108, A063112, A063113, A063543.

var stk: stack; end; for n := 1 to 80 do s := itoa(n); for j := 0 to length(s) -1 do k := atoi(s[j..j]); if k > 0 then stack_push(stk,k); end; end; write(n + product(stack2array(stk))," "); end;

a063114 n = n + a051801 n -- Reinhard Zumkeller, Jan 15 2012

Table[i+Times@@(IntegerDigits[i]/. 0->1), {i, 70}]

a(n) = n + vecprod(select(x->(x!=0), digits(n))) \\ Harry J. Smith, Aug 19 2009

a(n) = n + A051801(n). - Reinhard Zumkeller, Jan 15 2012

More terms from Robert G. Wilson v and Klaus Brockhaus, Aug 09 2001

A063113 a(1) = 1; a(n+1) = a(n) + product of nonzero digits of a(n) when written in base 3. But display sequence in base 10.

Original entry on oeis.org

1, 2, 4, 5, 7, 9, 10, 11, 13, 14, 16, 18, 20, 24, 28, 29, 31, 32, 34, 36, 37, 38, 40, 41, 43, 45, 47, 51, 55, 57, 59, 63, 65, 69, 73, 77, 85, 86, 88, 90, 91, 92, 94, 95, 97, 99, 101, 105, 109, 110, 112, 113, 115, 117, 118, 119, 121, 122, 124, 126, 128, 132, 136, 138

Offset: 1

N. J. A. Sloane, Aug 08 2001

Harry J. Smith, Table of n, a(n) for n = 1..1000
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. A063108, A063112, A063114.

f[n_Integer] := (a = Sort[ IntegerDigits[n, 3]]; While[ a[[1]] == 0, a = Delete[a, 1]]; n + Apply[ Times, a] ); NestList[f, 1, 65]

baseE(x, b)= { local(d,e,f); e=0; f=1; while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) }
ProdNzD(x)= { local(d,p); p=1; while (x>9, d=x-10*(x\10); if (d, p*=d); x\=10); return(p*x) }
{ for (n=1, 1000, if (n>1, a=baseE(b+= ProdNzD(a), 3), a=1; b=1); write("b063113.txt", n, " ", b) ) } \\ Harry J. Smith, Aug 19 2009

More terms from Robert G. Wilson v, Aug 09 2001

cp's OEIS Frontend

A063108 a(1) = 1; thereafter a(n+1) = a(n) + product of nonzero digits of a(n).

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A063114 a(n) = n + product of the nonzero digits of n.

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A063113 a(1) = 1; a(n+1) = a(n) + product of nonzero digits of a(n) when written in base 3. But display sequence in base 10.

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Extensions