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

1,2

Comments

All the terms are multiples of 4 (A008586).

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.

Example

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.

Mathematica

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

Crossrefs

Cf. A007623, A008586, A351894.

Subsequence: A052849 \ {2}.

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

Sequence in context: A374905 A253122 A239413 * A327295 A361418 A066632

Adjacent sequences: A351890 A351891 A351892 * A351894 A351895 A351896

Keyword

nonn,base

Author

Amiram Eldar, Feb 24 2022

Status

approved