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%I #19 Feb 07 2024 01:16:52
%S 0,2,4,6,7,8,10,12,13,14,16,18,19,20,22,24,25,26,27,28,29,30,31,32,34,
%T 36,37,38,40,42,43,44,46,48,49,50,51,52,53,54,55,56,58,60,61,62,64,66,
%U 67,68,70,72,73,74,75,76,77,78,79,80,82,84,85,86,88,90,91
%N Numbers n whose factorial base representation A007623(n) contains at least one nonleading zero. (Zero is also included as a(0)).
%H Antti Karttunen, <a href="/A227187/b227187.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%F a(0) = 0, a(1) = 2, and for n > 1, if a(n-1) is odd or A257510(a(n-1)) > 1, then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1) + 2. - _Antti Karttunen_, Apr 29 2015
%F Other identities:
%F For all n >= 2, a(A132371(n)) = A000142(n) = n! [See comments in A227157.]
%t q[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; MemberQ[s, 0]]; q[0] = True; Select[Range[0, 100], q] (* _Amiram Eldar_, Feb 07 2024 *)
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A227187 (ZERO-POS 0 0 A208575))
%o (definec (A227187 n) (if (<= n 1) (+ n n) (let ((prev (A227187 (- n 1)))) (cond ((odd? prev) (+ 1 prev)) ((> (A257510 prev) 1) (+ 1 prev)) (else (+ 2 prev))))))
%Y Complement: A227157.
%Y The sequence gives all positions n where A208575 is zero and all terms where A257510 (also A257260) are nonzeros.
%Y Cf. A232745 (a subsequence), A232744.
%Y Cf. also A007623, A132371, A153880, A227130, A227132, A256450 (numbers with at least one 1 in their factorial representation).
%K nonn,base
%O 0,2
%A _Antti Karttunen_, Jul 04 2013
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