A074233 - OEIS

%I #23 Jan 24 2022 09:43:40

%S 0,1,2,3,28,137,210,692,717,933,3138,3213,3416,3467,3538,16068

%N Numbers whose base-4 and base-5 representations are permutations of the same multiset of digits.

%C This sequence is finite and full. Proof: the smallest base-5 number with m digits is 5^(m-1). The largest base-4 number with m digits is 4^m - 1. For m >= 8, 5^(m-1) > 4^m - 1. So any term is <= 4^8 which has been checked. - _David A. Corneth_, Jan 24 2022

%e 692 is represented as 22310 in base 4 and as 10232 in base 5. Each representation is a permutation of the multiset {0,1,2,2,3}.

%o (PARI) isok(m) = vecsort(digits(m, 4)) == vecsort(digits(m, 5)); \\ _Michel Marcus_, Jan 24 2022

%Y Cf. A007090, A007091, A037423.

%K base,nonn,fini,full

%O 1,3

%A _Paul Lusch_, Sep 18 2002

%E First four terms inserted by _David A. Corneth_, Jan 24 2022