A091077 Numbers n which when converted to base 3, reversed and converted back to base 10 yield a number m such that n mod m = 0. Cases which are trivial or result in digit loss are excluded.

64, 208, 640, 1936, 5248, 5824, 15616, 17488, 46720, 50752, 52480, 140032, 151840, 157456, 419968, 425152, 455104, 467200, 472384, 1259776, 1276624, 1364896, 1400320, 1417168, 3779200, 3794752, 3831040, 4094272, 4109824, 4199680, 4235968, 4251520

Offset: 1

Author

Chuck Seggelin, Dec 18 2003

Keywords

• base
• nonn

Comments

Trivial cases are those numbers which upon conversion result in a number which is palindromic (m = reverse(m)), or a palindrome plus trailing zeros such that m = reverse(m)*10^z where z=number of lost zeros. Nontrivial digit loss occurs when a converted number has trailing zeros that drop off when the number is reversed.

Examples

			a(1) = 64 because: 64 in base 3 is 2101; 2101 reversed is 1012; 1012 converted back to base 10 is 32 and 64 mod 32 = 0.
		

Links

• C. Seggelin, Numbers Divisible by Digit Permutations. [Broken link]

Crossrefs

Cf. A091078 (same in base 4), A091079 (base 5), A091080 (base 6), A091081 (base 7), A091082 (base 8), A091083 (base 9), A031877 (base 10).

Programs

PARI

isok(n, b=3) = {m = subst(Polrev(digits(n, b)), x, b); if (n % m, return(0));if ((n/m == 1), return (0)); vq = valuation(n, b); if (! vq, return (1)); qq = subst(Polrev(digits(m,b)), x, b); if (n == b^vq*qq, return (0)); return (1);} \\ Michel Marcus, Oct 10 2014

Extensions

More terms from Michel Marcus, Oct 10 2014