A232742 - OEIS

%I #14 Dec 05 2013 08:35:20

%S 6,12,18,30,36,42,54,60,66,78,84,90,102,108,114,120,126,132,138,150,

%T 156,162,174,180,186,198,204,210,222,228,234,240,246,252,258,270,276,

%U 282,294,300,306,318,324,330,342,348,354,360,366,372,378,390,396,402,414

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

%C Numbers n for which A055881(n) is one of the terms of A072668.

%C Equally: numbers n for which {the number of the trailing zeros in their factorial base representation A007623(n)} + 2 is a composite number.

%C All terms are divisible by 6.

%C 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 Antti Karttunen, <a href="/A232742/b232742.txt">Table of n, a(n) for n = 1..10656</a>

%e 6 is included because A055881(6)=3 and 3+1 is a composite number.

%e 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 120 is the first included multiple of 24, as A055881(120)=5 and 6 is a composite.

%o (Scheme, with Antti Karttunen's IntSeq-library)

%o (define A232742 (MATCHING-POS 1 1 (lambda (n) (not (prime? (+ 1 (A055881 n)))))))

%Y Complement: A232741. Subset: A232743.

%Y Cf. A055926, A232744-A232745, A007623, A055881, A230403.

%K nonn

%O 1,1

%A _Antti Karttunen_, Dec 01 2013