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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.
0
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
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
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