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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.
7
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.
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
KEYWORD
base,nonn
AUTHOR
Chuck Seggelin (barkeep(AT)plastereddragon.com), Dec 18 2003
EXTENSIONS
More terms from Michel Marcus, Oct 10 2014
STATUS
approved