cp's OEIS Frontend

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.

%I A235031 #18 May 09 2021 02:16:06
%S A235031 2,1,26,28,66,289,579,3468,23889,2366688,45579999,356688888888,
%T A235031 35888888888888889,2455566666777777999999999999999
%N 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.
%C A235031 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.
%C A235031 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
%e A235031 For n=18: 1, 2, 4, 8, 16, 13, 7, 14, 9, 18, 17, 15, 11, 3, 6, 12, 5, 10.
%e A235031 For n=19: 26, 20, 4, 8, 16, 13, 7, 14, 9, 18, 17, 15, 11, 3, 6, 12, 5, 10, 2.
%o A235031 (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])
%o A235031 len(n)=my(v=Set([n])); while(1,n=step(n); if(setsearch(v,n), return(#v)); v=setunion(v,Set([n])))
%o A235031 a(n)=my(k);while(len(k++)!=n,); k \\ _Charles R Greathouse IV_, Jan 02 2014
%Y A235031 Cf. A007953, A007954, A061762.
%K A235031 nonn,base
%O A235031 17,1
%A A235031 _Carlos Rivera_, Jan 02 2014
%E A235031 a(17) and a(27)-a(30) from _Giovanni Resta_, Jan 02 2014