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

1,1

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.

Links

Table of n, a(n) for n=1..32.

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

Example

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.

Prog

(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

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).

Sequence in context: A320338 A250135 A273321 * A245991 A186637 A295021

Adjacent sequences: A091074 A091075 A091076 * A091078 A091079 A091080

Keyword

base,nonn

Author

Chuck Seggelin (barkeep(AT)plastereddragon.com), Dec 18 2003

Extensions

More terms from Michel Marcus, Oct 10 2014

Status

approved