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.

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

Author

N. J. A. Sloane, Aug 08 2001

Keywords

• nonn
• base

Links

• 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

Crossrefs

Cf. A063108, A063112, A063114.

Programs

Mathematica

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

PARI

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

Extensions

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