A243102 Numbers n such that the digits of (n + product of digits of n) are a nontrivial permutation of the digits of n.

239, 326, 364, 497, 563, 598, 613, 637, 695, 819, 1239, 1326, 1364, 1497, 1563, 1598, 1613, 1637, 1695, 1819, 2139, 2313, 2356, 2369, 2419, 2594, 2639, 2791, 3126, 3213, 3235, 3238, 3259, 3354, 3365, 3561, 4219, 4346, 4353, 4395, 4559, 4569, 4592, 4595, 4719, 4953, 4967, 5129, 5233

Offset

1,1

Comments

The product of digits must be divisible by 9, but is not 0. - Robert Israel, Aug 24 2014

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Example

239 + 2*3*9 = 293 is a permutation of the digits of 239. Thus 239 is a member of this sequence.

Maple

filter:= proc(n)
local L, m;
L:= convert(n, base, 10);
m:= convert(L, `*`);
if m=0 then return false fi;
sort(L) = sort(convert(n+m, base, 10));
end proc:
select(filter, [$1..1000]); # Robert Israel, Aug 24 2014

Prog

(PARI) for(n=1, 10^5, d=digits(n); p=prod(i=1, #d, d[i]); v=digits(n+p); if(v!=d, v=vecsort(v); d=vecsort(d); if(v==d, print1(n, ", "))))
(Python)
from operator import mul
from functools import reduce
A243102 = [int(n) for n in (str(x) for x in range(1, 10**5)) if not n.count('0') and sorted(str(int(n)+reduce(mul, (int(d) for d in n)))) == sorted(n)]
# Chai Wah Wu, Aug 26 2014

Crossrefs

Cf. A007954.

Sequence in context: A140032 A289109 A247888 * A294092 A056086 A046012

Adjacent sequences: A243099 A243100 A243101 * A243103 A243104 A243105

Keyword

nonn,base

Author

Derek Orr, Aug 19 2014

Extensions

Definition edited by Robert Israel, Aug 24 2014

Status

approved