cp's OEIS Frontend

A091078 Numbers n which when converted to base 4, 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 A091078 #6 Jun 08 2025 16:15:42
%S A091078 225,945,3825,15345,57825,61425,230625,245745,921825,968625,983025,
%T A091078 368,6625,3871665,3932145,14745825,14803425,15483825,15671025,
%U A091078 15728625,589826,25,59224545,61932465,62672625,62914545
%N A091078 Numbers n which when converted to base 4, 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 A091078 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 A091078 C. Seggelin, <a href="http://www.plastereddragon.com/maths/asortdiv.htm">Numbers Divisible by Digit Permutations</a>. [Broken link]
%e A091078 a(1) = 225 because: 225 in base 4 is 3201; 3201 reversed is 1023; 1023 converted back to base 10 is 75 and 225 mod 75 = 0.
%o A091078 (PARI) /* See A091077 and use PARI script with b=4 */
%Y A091078 Cf. A091077 (same in base 3), A091079 (base 5), A091080 (base 6), A091081 (base 7), A091082 (base 8), A091083 (base 9), A031877 (base 10).
%K A091078 base,nonn
%O A091078 1,1
%A A091078 _Chuck Seggelin_, Dec 18 2003
%E A091078 More terms from _Michel Marcus_, Oct 10 2014