A351895 Numbers with an equal number of odd and even digits in their factorial-base representation.

2, 5, 25, 26, 29, 30, 34, 37, 38, 41, 42, 46, 51, 55, 56, 59, 63, 67, 68, 71, 73, 74, 77, 78, 82, 85, 86, 89, 90, 94, 99, 103, 104, 107, 111, 115, 116, 119, 723, 727, 728, 731, 735, 739, 740, 743, 745, 746, 749, 750, 754, 757, 758, 761, 762, 766, 771, 775, 776

Offset: 1

Author

Amiram Eldar, Feb 24 2022

Keywords

• nonn
• base

Examples

			5 is a term since its factorial-base representation, 21, has one odd digit, 1, and one even digit, 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Wikipedia, Factorial number system.
• Index entries for sequences related to factorial base representation.

Crossrefs

Cf. A007623, A351893, A351894.

A138524 is a subsequence.

Similar sequences: A031443 (binary), A227870 (decimal).

Programs

Mathematica

max = 7; fctBaseDigits[n_] := IntegerDigits[n, MixedRadix[Range[max, 2, -1]]]; Select[Range[1, max!], EvenQ[Length[(d = fctBaseDigits[#])]] && Count[d, _?EvenQ] == Length[d]/2 &]