A351896 Numbers k such that k and k+2 both have an equal number of odd and even digits in their factorial-base representations.

71, 743, 791, 839, 862, 910, 983, 1031, 1079, 1102, 1150, 1223, 1271, 1319, 1342, 1390, 1583, 1631, 1823, 1871, 2063, 2111, 2183, 2231, 2279, 2302, 2350, 2423, 2471, 2519, 2542, 2590, 2663, 2711, 2759, 2782, 2830, 3023, 3071, 3263, 3311, 3503, 3551, 3623, 3671, 3719

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Wikipedia, Factorial number system.

Index entries for sequences related to factorial base representation.

Example

71 is a term since the factorial-base representations of 71 and 73 are 2321 and 3001, respectively, and both have 2 odd digits and 2 even digits.

Mathematica

max = 7; fctBaseDigits[n_] := IntegerDigits[n, MixedRadix[Range[max, 2, -1]]]; s = Select[Range[1, max!], EvenQ[Length[(d = fctBaseDigits[#])]] && Count[d, _?EvenQ] == Length[d]/2 &]; ind = Position[Differences[s], 2] // Flatten; s[[ind]]

Crossrefs

Subsequence of A351895.

Cf. A007623, A351893, A351894.

Similar sequence: A337238.

Sequence in context: A201039 A142674 A112750 * A089706 A220623 A173806

Adjacent sequences: A351893 A351894 A351895 * A351897 A351898 A351899

Keyword

nonn,base

Author

Amiram Eldar, Feb 24 2022

Status

approved