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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

%I

%S 71,743,791,839,862,910,983,1031,1079,1102,1150,1223,1271,1319,1342,

%T 1390,1583,1631,1823,1871,2063,2111,2183,2231,2279,2302,2350,2423,

%U 2471,2519,2542,2590,2663,2711,2759,2782,2830,3023,3071,3263,3311,3503,3551,3623,3671,3719

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

%H Amiram Eldar, <a href="/A351896/b351896.txt">Table of n, a(n) for n = 1..10000</a>

%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 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.

%t 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]]

%Y Subsequence of A351895.

%Y Cf. A007623, A351893, A351894.

%Y Similar sequence: A337238.

%K nonn,base

%O 1,1

%A _Amiram Eldar_, Feb 24 2022

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Last modified August 14 12:15 EDT 2022. Contains 356116 sequences. (Running on oeis4.)