cp's OEIS Frontend

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.

%I A091077 #9 Jun 08 2025 16:15:42
%S A091077 64,208,640,1936,5248,5824,15616,17488,46720,50752,52480,140032,
%T A091077 151840,157456,419968,425152,455104,467200,472384,1259776,1276624,
%U A091077 1364896,1400320,1417168,3779200,3794752,3831040,4094272,4109824,4199680,4235968,4251520
%N 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.
%C A091077 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.
%H A091077 C. Seggelin, <a href="http://www.plastereddragon.com/maths/asortdiv.htm">Numbers Divisible by Digit Permutations</a>. [Broken link]
%e A091077 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.
%o A091077 (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
%Y A091077 Cf. A091078 (same in base 4), A091079 (base 5), A091080 (base 6), A091081 (base 7), A091082 (base 8), A091083 (base 9), A031877 (base 10).
%K A091077 base,nonn
%O A091077 1,1
%A A091077 _Chuck Seggelin_, Dec 18 2003
%E A091077 More terms from _Michel Marcus_, Oct 10 2014