A117057 Palindromes which are divisible by the product of their digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 111, 212, 1111, 2112, 4224, 11111, 11711, 13131, 21112, 21312, 31113, 42624, 111111, 211112, 234432, 1111111, 1113111, 2111112, 2112112, 2114112, 2118112, 11111111, 21111112, 21122112, 61111116, 111111111

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 16 2006

Keywords

• base
• nonn

Comments

Are there infinitely many terms that do not contain a 1? - Derek Orr, Aug 26 2014

Examples

			4224 is in the sequence because (1) it is a palindrome, (2) the product of its digits is 4*2*2*4=64 and 4224 is divisible by 64.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..221

Crossrefs

Cf. A002113.

Programs

Mathematica

fQ[n_] := Block[{id = IntegerDigits@n}, Reverse@id == id && Count[id, 0] == 0 && Mod[n, Times @@ id] == 0]; Do[ If[ fQ@n, Print@n], {n, 10^7}] (* Robert G. Wilson v *)

PARI

{m=120000000;for(n=1,m,k=n;rev=0;while(k>0,d=divrem(k,10);k=d[1];rev=10*rev+d[2]); if(n==rev,p=1;h=n;while(h>0,d=divrem(h,10);h=d[1];p=p*d[2]);if(p>0&&n%p==0,print1(n,","))))} \\ Klaus Brockhaus, Apr 17 2006

Python

from operator import mul
from functools import reduce
from gmpy2 import t_mod, mpz
A117057 = sorted([mpz(n) for n in (str(x)+str(x)[::-1] for x in range(1,10**6))
        if not (n.count('0') or t_mod(mpz(n), reduce(mul,(mpz(d) for d in n))))]+
        [mpz(n) for n in (str(x)+str(x)[-2::-1] for x in range(10**6))
        if not (n.count('0') or t_mod(mpz(n), reduce(mul,(mpz(d) for d in n))))])
# Chai Wah Wu, Aug 26 2014

Extensions

a(23) to a(36) from Klaus Brockhaus, Apr 17 2006