A242948 Numbers k such that A = k+DigitProd(k) is divisible by the largest power of 10 <= A.

1, 2, 3, 4, 5, 15, 35, 42, 44, 46, 48, 55, 91, 191, 272, 337, 692, 919, 1919, 2488, 5775, 7795, 7984, 17795, 17984, 28464, 29424, 394816, 489632, 683872, 3992224, 4996112, 7872992, 29927424, 89668224, 7991871488, 9968647168, 9991319797

Offset: 1

Author

Derek Orr, May 27 2014

Keywords

• nonn
• base
• hard

Comments

Trivially, numbers in A037124 satisfy this but are not included in this sequence.

It is not known if a(n) is infinite.

a(54) (if it exists) is > 10^49. - Hiroaki Yamanouchi, Jul 10 2014

Examples

			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.
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..53

Crossrefs

Cf. A037124, A055642, A007954.

Programs

PARI

DP(n)={p=1; d= digits(n); for(i=1,#d,p*=d[i]);return(p)}
for(n=1,10^7,if(n%10!=0&&(n+DP(n))%10^(#Str(n+DP(n))-1)==0,print1(n,", ")))

Extensions

a(34)-a(38) from Hiroaki Yamanouchi, Jul 10 2014