

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 member of the sequence. PD is the product of the nonzero digits; SD is the sum of the digits.


0



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

17,1


COMMENTS

If X is a previous member of the sequence greater than zero and less than 10, then PD=X and SD=X and so the next member 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: A087452 A317385 A098878 * A138955 A089963 A322230
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



