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A232745 Numbers k for which the largest m such that m! divides k is even.

%I A232745 #13 Feb 26 2021 20:12:14
%S A232745 2,4,8,10,14,16,20,22,24,26,28,32,34,38,40,44,46,48,50,52,56,58,62,64,
%T A232745 68,70,72,74,76,80,82,86,88,92,94,96,98,100,104,106,110,112,116,118,
%U A232745 122,124,128,130,134,136,140,142,144,146,148,152,154,158,160,164
%N A232745 Numbers k for which the largest m such that m! divides k is even.
%C A232745 Numbers k for which A055881(k) is even.
%C A232745 Equally: Numbers k which have an odd number of the trailing zeros in their factorial base representation A007623(k).
%C A232745 The sequence can be described in the following manner: Sequence includes all multiples of 2! (even numbers), except that it excludes from those the multiples of 3! (6), except that it includes the multiples of 4! (24), except that it excludes the multiples of 5! (120), except that it includes the multiples of 6! (720), except that it excludes the multiples of 7! (5040), except that it includes the multiples of 8! (40320), except that it excludes the multiples of 9! (362880), except that it includes the multiples of 10! (3628800), except that ..., ad infinitum.
%C A232745 The number of terms not exceeding m! for m>=1 is A000166(m). The asymptotic density of this sequence is 1/e (A068985). - _Amiram Eldar_, Feb 26 2021
%H A232745 Antti Karttunen, <a href="/A232745/b232745.txt">Table of n, a(n) for n = 1..14833</a>
%t A232745 seq[max_] := Select[Range[max!], OddQ @ LengthWhile[Reverse @ IntegerDigits[#, MixedRadix[Range[max, 2, -1]]], #1 == 0 &] &]; seq[5] (* _Amiram Eldar_, Feb 26 2021 *)
%o A232745 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A232745 (define A232745 (MATCHING-POS 1 1 (lambda (n) (even? (A055881 n)))))
%Y A232745 Complement: A232744.
%Y A232745 b(n) = A153880(A232744(n)) gives a subset of this sequence.
%Y A232745 Cf. also A055881, A007623, A232741-A232743.
%Y A232745 Analogous sequences for binary system: A003159 & A036554.
%Y A232745 Cf. A000166, A068985.
%K A232745 nonn
%O A232745 1,1
%A A232745 _Antti Karttunen_, Dec 01 2013