cp's OEIS Frontend

A091083 Numbers n which when converted to base 9, 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 A091083 #6 Jun 08 2025 16:15:42
%S A091083 64,640,4800,5248,5824,6400,43680,46720,52480,58240,393600,419968,
%T A091083 425152,467200,472384,524800,3542880,3779200,3831040,4199680,4251520,
%U A091083 4723840,31497600,31886400,34012288,34058944,34437376,34484032,37792000,37838656,38217088
%N A091083 Numbers n which when converted to base 9, 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 A091083 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 A091083 C. Seggelin, <a href="http://www.plastereddragon.com/maths/asortdiv.htm">Numbers Divisible by Digit Permutations</a>. [Broken link]
%e A091083 a(1) = 64 because 64 in base 9 is 71; 71 reversed is 17; 17 converted back to base 10 is 16 and 64 mod 16 = 0.
%o A091083 (PARI) /* See A091077 and use PARI script with b=9 */
%Y A091083 Cf. A091077 (same in base 3), A091078 (base 4), A091079 (base 5), A091080 (base 6), A091081 (base 7), A091082 (base 8), A031877 (base 10).
%K A091083 base,nonn
%O A091083 1,1
%A A091083 _Chuck Seggelin_, Dec 18 2003
%E A091083 More terms from _Michel Marcus_, Oct 10 2014