A351893 Numbers that contain only even digits in their factorial-base representation.

0, 4, 12, 16, 48, 52, 60, 64, 96, 100, 108, 112, 240, 244, 252, 256, 288, 292, 300, 304, 336, 340, 348, 352, 480, 484, 492, 496, 528, 532, 540, 544, 576, 580, 588, 592, 1440, 1444, 1452, 1456, 1488, 1492, 1500, 1504, 1536, 1540, 1548, 1552, 1680, 1684, 1692, 1696

Offset: 1

Author

Amiram Eldar, Feb 24 2022

Keywords

• nonn
• base

Comments

All the terms are multiples of 4 (A008586).

Examples

			4 is a term since its factorial-base presentation, 20, has only even digits.
16 is a term since its factorial-base presentation, 220, has only even digits.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..14400 (terms below 10!)
• Wikipedia, Factorial number system.
• Index entries for sequences related to factorial base representation.

Crossrefs

Cf. A007623, A008586, A351894.

Subsequence: A052849 \ {2}.

Similar sequences: A005823 (ternary), A014263 (decimal), A062880 (quaternary).

Programs

Mathematica

max = 7; fctBaseDigits[n_] := IntegerDigits[n, MixedRadix[Range[max, 2, -1]]]; Select[Range[0, max!, 2], AllTrue[fctBaseDigits[#], EvenQ] &]