A351894 Numbers that contain only odd digits in their factorial-base representation.

1, 3, 9, 21, 33, 45, 81, 93, 153, 165, 201, 213, 393, 405, 441, 453, 633, 645, 681, 693, 873, 885, 921, 933, 1113, 1125, 1161, 1173, 1353, 1365, 1401, 1413, 2313, 2325, 2361, 2373, 2553, 2565, 2601, 2613, 2793, 2805, 2841, 2853, 3753, 3765, 3801, 3813, 3993, 4005

Offset: 1

Author

Amiram Eldar, Feb 24 2022

Keywords

• nonn
• base

Comments

All the terms above 1 are odd multiples of 3.

Examples

			3 is a term since its factorial-base presentation, 11, has only odd digits.
21 is a term since its factorial-base presentation, 311, has only odd digits.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..18056 (terms below 11!)
• Wikipedia, Factorial number system.
• Index entries for sequences related to factorial base representation.

Crossrefs

Cf. A007623, A016945, A351893.

Subsequence: A007489

Similar sequences: A003462 \ {0} (ternary), A014261 (decimal), A032911 (base 4), A032912 (base 5), A033032 (base 6), A033033 (base 7), A033034 (base 8), A033035 (base 9), A033036 (base 11), A033037 (base 12), A033038 (base 13), A033039 (base 14), A033040 (base 15), A033041 (base 16), A126646 (binary).

Programs

Mathematica

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