A117228 Palindromes which are divisible by the product and by the sum of their digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 111, 2112, 4224, 13131, 21112, 21312, 31113, 42624, 211112, 234432, 1113111, 2111112, 2114112, 2118112, 21122112, 61111116, 111111111, 211121112, 211242112, 211262112, 213141312, 2111111112, 2112332112, 2114114112, 2131221312

Offset: 1

Author

Giovanni Resta, Apr 22 2006

Keywords

• base
• nonn

Comments

Intersection of A082232 and A117057.

Are there infinitely many terms that don't contain a 1? - Derek Orr, Aug 25 2014

Examples

			42624 is divisible by 4*2*6*2*4 and by 4+2+6+2+4.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..91

Crossrefs

Cf. A002113, A082232, A117057.

Programs

PARI

rev(n)=r="";d=digits(n);for(i=1,#d,r=concat(Str(d[i]),r));eval(r)
for(n=1,10^7,d=digits(n);if(rev(n)==n,p=prod(i=1,#d,d[i]);if(p&&n%p==0&&n%sumdigits(n)==0,print1(n,", ")))) \\ Derek Orr, Aug 25 2014

Python

from operator import mul
from functools import reduce
from gmpy2 import t_mod, mpz
A117228 = sorted([mpz(n) for n in (str(x)+str(x)[::-1] for x in range(1, 10**8))
          if not (n.count('0') or t_mod(mpz(n), sum((mpz(d) for d in n)))
          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**8))
          if not (n.count('0') or t_mod(mpz(n), sum((mpz(d) for d in n)))
          or t_mod(mpz(n), reduce(mul, (mpz(d) for d in n))))])
# Chai Wah Wu, Aug 25 2014

Extensions

More terms from Chai Wah Wu, Aug 22 2014