A235031 The first integer that produces a sequence of n terms without repetition. Any term of the sequence, after the first one, is the sum of PD and SD of the previous term of the sequence. PD is the product of the nonzero digits; SD is the sum of the digits.

2, 1, 26, 28, 66, 289, 579, 3468, 23889, 2366688, 45579999, 356688888888, 35888888888888889, 2455566666777777999999999999999

Offset

17,1

Comments

If X is a previous term of the sequence greater than zero and less than 10, then PD=X and SD=X and so the next term is 2X.

The values of a(n) for n = 1..12 are 19, 34, 46, 177, 458, 2699, 279999, 4557888, 23366667799, 456667788889999, 246666666666666667888999, and 23777777777777777888888888899999999. - Giovanni Resta, Jan 02 2014

Links

Table of n, a(n) for n=17..30.

Example

For n=18: 1, 2, 4, 8, 16, 13, 7, 14, 9, 18, 17, 15, 11, 3, 6, 12, 5, 10.
For n=19: 26, 20, 4, 8, 16, 13, 7, 14, 9, 18, 17, 15, 11, 3, 6, 12, 5, 10, 2.

Prog

(PARI) step(n)=my(d=digits(n), D=select(k->k>1, d)); sum(i=1, #d, d[i]) + prod(i=1, #D, D[i])
len(n)=my(v=Set([n])); while(1, n=step(n); if(setsearch(v, n), return(#v)); v=setunion(v, Set([n])))
a(n)=my(k); while(len(k++)!=n, ); k \\ Charles R Greathouse IV, Jan 02 2014

Crossrefs

Cf. A007953, A007954, A061762.

Sequence in context: A317385 A366048 A098878 * A138955 A089963 A362013

Adjacent sequences: A235028 A235029 A235030 * A235032 A235033 A235034

Keyword

nonn,base

Author

Carlos Rivera, Jan 02 2014

Extensions

a(17) and a(27)-a(30) from Giovanni Resta, Jan 02 2014

Status

approved