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

Author

Carlos Rivera, Jan 02 2014

Keywords

• nonn
• base

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

Examples

			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.
		

Crossrefs

Cf. A007953, A007954, A061762.

Programs

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

Extensions

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