cp's OEIS Frontend

A232744 Numbers k for which the largest m such that m! divides k is odd.

%I A232744 #16 Feb 26 2021 20:12:08
%S A232744 1,3,5,6,7,9,11,12,13,15,17,18,19,21,23,25,27,29,30,31,33,35,36,37,39,
%T A232744 41,42,43,45,47,49,51,53,54,55,57,59,60,61,63,65,66,67,69,71,73,75,77,
%U A232744 78,79,81,83,84,85,87,89,90,91,93,95,97,99,101,102,103,105
%N A232744 Numbers k for which the largest m such that m! divides k is odd.
%C A232744 Numbers k for which A055881(k) is odd.
%C A232744 Equally: Numbers k which have an even number of the trailing zeros in their factorial base representation A007623(k).
%C A232744 The sequence can be described in the following manner: Sequence includes all multiples of 1!, except that it excludes from those the multiples of 2!, except that it includes the multiples of 3! (6), except that it excludes the multiples of 4! (24), except that it includes the multiples of 5! (120), except that it excludes the multiples of 6! (720), except that it includes the multiples of 7! (5040), except that it excludes the multiples of 8! (40320), except that it includes the multiples of 9! (362880), and so on, ad infinitum.
%C A232744 The number of terms not exceeding m! for m>=1 is A002467(m). The asymptotic density of this sequence is 1 - 1/e (A068996). - _Amiram Eldar_, Feb 26 2021
%H A232744 Antti Karttunen, <a href="/A232744/b232744.txt">Table of n, a(n) for n = 1..9558</a>
%F A232744 a(1)=1, and for n>1, a(n) = a(n-1) + (2 - A000035(A055881(a(n-1)+1))).
%t A232744 seq[max_] := Select[Range[max!], EvenQ @ LengthWhile[Reverse @ IntegerDigits[#, MixedRadix[Range[max, 2, -1]]], #1 == 0 &] &]; seq[5] (* _Amiram Eldar_, Feb 26 2021 *)
%o A232744 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A232744 (define A232744 (MATCHING-POS 1 1 (lambda (n) (odd? (A055881 n)))))
%o A232744 ;; Alternative implementation with a simple recurrence:
%o A232744 (definec (A232744 n) (if (<= n 1) n (+ (A232744 (- n 1)) (- 2 (A000035 (A055881 (+ 1 (A232744 (- n 1)))))))))
%Y A232744 Complement: A232745. Cf. also A055881, A007623, A232741-A232743.
%Y A232744 Analogous sequences for binary system: A003159 & A036554.
%Y A232744 Cf. A002467, A068996.
%K A232744 nonn
%O A232744 1,2
%A A232744 _Antti Karttunen_, Dec 01 2013