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%I #18 Nov 09 2024 06:16:16
%S 1,2,3,4,5,15,35,42,44,46,48,55,91,191,272,337,692,919,1919,2488,5775,
%T 7795,7984,17795,17984,28464,29424,394816,489632,683872,3992224,
%U 4996112,7872992,29927424,89668224,7991871488,9968647168,9991319797
%N Numbers k such that A = k+DigitProd(k) is divisible by the largest power of 10 <= A.
%C Trivially, numbers in A037124 satisfy this but are not included in this sequence.
%C It is not known if a(n) is infinite.
%C a(54) (if it exists) is > 10^49. - _Hiroaki Yamanouchi_, Jul 10 2014
%H Hiroaki Yamanouchi, <a href="/A242948/b242948.txt">Table of n, a(n) for n = 1..53</a>
%e 272+2*7*2 = 300 is divisible by the highest power of 10 lower than 300 (in this case, 100). Thus 272 is a member of this sequence.
%o (PARI) DP(n)={p=1; d= digits(n); for(i=1,#d,p*=d[i]);return(p)}
%o for(n=1,10^7,if(n%10!=0&&(n+DP(n))%10^(#Str(n+DP(n))-1)==0,print1(n,", ")))
%Y Cf. A037124, A055642, A007954.
%K nonn,base,hard
%O 1,2
%A _Derek Orr_, May 27 2014
%E a(34)-a(38) from _Hiroaki Yamanouchi_, Jul 10 2014