A235031 - OEIS

%I #18 May 09 2021 02:16:06

%S 2,1,26,28,66,289,579,3468,23889,2366688,45579999,356688888888,

%T 35888888888888889,2455566666777777999999999999999

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

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

%o (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 len(n)=my(v=Set([n])); while(1,n=step(n); if(setsearch(v,n), return(#v)); v=setunion(v,Set([n])))

%o a(n)=my(k);while(len(k++)!=n,); k \\ _Charles R Greathouse IV_, Jan 02 2014

%Y Cf. A007953, A007954, A061762.

%K nonn,base

%O 17,1

%A _Carlos Rivera_, Jan 02 2014

%E a(17) and a(27)-a(30) from _Giovanni Resta_, Jan 02 2014