A074233 Numbers whose base-4 and base-5 representations are permutations of the same multiset of digits.

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

Offset: 1

Author

Paul Lusch, Sep 18 2002

Keywords

• base
• nonn
• fini
• full

Comments

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

Examples

			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}.
		

Crossrefs

Cf. A007090, A007091, A037423.

Programs

PARI

isok(m) = vecsort(digits(m, 4)) == vecsort(digits(m, 5)); \\ Michel Marcus, Jan 24 2022

Extensions

First four terms inserted by David A. Corneth, Jan 24 2022