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

1,2

Comments

All the terms above 1 are odd multiples of 3.

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.

Example

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.

Mathematica

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

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).

Sequence in context: A331131 A089322 A182632 * A286590 A061978 A031886

Adjacent sequences: A351891 A351892 A351893 * A351895 A351896 A351897

Keyword

nonn,base

Author

Amiram Eldar, Feb 24 2022

Status

approved