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A232742 Numbers n for which the largest m such that (m-1)! divides n is a composite.

%I A232742 #18 May 16 2025 02:11:42
%S A232742 6,12,18,30,36,42,54,60,66,78,84,90,102,108,114,120,126,132,138,150,
%T A232742 156,162,174,180,186,198,204,210,222,228,234,240,246,252,258,270,276,
%U A232742 282,294,300,306,318,324,330,342,348,354,360,366,372,378,390,396,402,414
%N A232742 Numbers n for which the largest m such that (m-1)! divides n is a composite.
%C A232742 Numbers n for which A055881(n) is one of the terms of A072668.
%C A232742 Equally: numbers n for which {the number of the trailing zeros in their factorial base representation A007623(n)} + 2 is a composite number.
%C A232742 All terms are divisible by 6.
%C A232742 The sequence can be described in the following manner: Sequence includes all multiples of 3!, except that it excludes from those 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) (and also those of 8! and 9!, because here 8+1 = 9 is the first odd composite), of which it however excludes the multiples of 10!, except that it includes the multiples of 11!, but excludes the multiples of 12!, but includes the multiples of 13! (and 14! and 15!, because 14-16 are all composites), but excludes the multiples of 16!, and so on, ad infinitum.
%H A232742 Antti Karttunen, <a href="/A232742/b232742.txt">Table of n, a(n) for n = 1..10656</a>
%e A232742 6 is included because A055881(6)=3 and 3+1 is a composite number.
%e A232742 24 is the first excluded multiple of 6, as A055881(24)=4 and 5 is a prime, not composite, so 24 is not included in this sequence.
%e A232742 120 is the first included multiple of 24, as A055881(120)=5 and 6 is a composite.
%o A232742 (Scheme, with Antti Karttunen's IntSeq-library)
%o A232742 (define A232742 (MATCHING-POS 1 1 (lambda (n) (not (prime? (+ 1 (A055881 n)))))))
%Y A232742 Complement: A232741. Subset: A232743.
%Y A232742 Cf. A055926, A232744-A232745, A007623, A055881, A230403.
%K A232742 nonn
%O A232742 1,1
%A A232742 _Antti Karttunen_, Dec 01 2013