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A351896 Numbers k such that k and k+2 both have an equal number of odd and even digits in their factorial-base representations. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 29 20:36 EDT 2022. Contains 354913 sequences. (Running on oeis4.)