

A242948


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


2



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
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OFFSET

1,2


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


LINKS

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


EXAMPLE

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.


PROG

(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, ", ")))


CROSSREFS

Cf. A037124, A055642, A007954.
Sequence in context: A183528 A145029 A145030 * A102738 A098553 A132705
Adjacent sequences: A242945 A242946 A242947 * A242949 A242950 A242951


KEYWORD

nonn,base,hard


AUTHOR

Derek Orr, May 27 2014


EXTENSIONS

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


STATUS

approved



