|
%I #11 Feb 26 2022 10:11:14
%S 0,4,12,16,48,52,60,64,96,100,108,112,240,244,252,256,288,292,300,304,
%T 336,340,348,352,480,484,492,496,528,532,540,544,576,580,588,592,1440,
%U 1444,1452,1456,1488,1492,1500,1504,1536,1540,1548,1552,1680,1684,1692,1696
%N Numbers that contain only even digits in their factorial-base representation.
%C All the terms are multiples of 4 (A008586).
%H Amiram Eldar, <a href="/A351893/b351893.txt">Table of n, a(n) for n = 1..14400</a> (terms below 10!)
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Factorial_number_system">Factorial number system</a>.
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%e 4 is a term since its factorial-base presentation, 20, has only even digits.
%e 16 is a term since its factorial-base presentation, 220, has only even digits.
%t max = 7; fctBaseDigits[n_] := IntegerDigits[n, MixedRadix[Range[max, 2, -1]]]; Select[Range[0, max!, 2], AllTrue[fctBaseDigits[#], EvenQ] &]
%Y Cf. A007623, A008586, A351894.
%Y Subsequence: A052849 \ {2}.
%Y Similar sequences: A005823 (ternary), A014263 (decimal), A062880 (quaternary).
%K nonn,base
%O 1,2
%A _Amiram Eldar_, Feb 24 2022
|
