proposed

approved

editing

proposed

The sequence is completely can be described by applying the principle of inclusion-exclusion in the following manner. : Sequence includes all multiples of 1! and 2! (odd and 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) (and also those of 8! and 9!) because here 8+1 = 9 is the first odd composite), except that it includes the multiples of 10!, but excludes the multiples of 11!, but includes the multiples of 12!, but excludes the multiples of 13! (and also of 14! and 15!, because 14-16 are all composites), but includes the multiples of 16!, and so on, ad infinitum.

Antti Karttunen, <a href="/A232741/b232741.txt">Table of n, a(n) for n = 1..8748</a>

Equally: Numbers n for which two plus {the number of the trailing zeros in their factorial base representation A007623(n) } + 2 is a prime.

The sequence is completely described by applying the principle of inclusion-exclusion in the following manner. Sequence includes all multiples of 1! and 2! (odd and 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) (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 1110!, but excludes the multiples of 1211!, but includes the multiples of 12!, but excludes the multiples of 13! (and also of 14! and 15!, because 14-16 are all composites), but excludes includes the multiples of 1516!, and so on, ad infinitum.

Equally: numbers Numbers n in whose factorial base representation A007623for which A055881(n) there are prime-2 trailing zerosis one of the terms of A006093.

Equally: Numbers n for which two plus the number of the trailing zeros in their factorial base representation A007623(n) is a prime.

The sequence is completely described by applying the principle of inclusion-exclusion in the following manner. Sequence includes all multiples of 1! and 2! (odd and 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) (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 15!, and so on, ad infinitum.

Complement: A232742. Cf. A055926, A232744-A232745, A007623, A055881, A230403.

allocated Numbers n for Antti Karttunenwhich the largest m such that (m-1)! divides n is a prime.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76

1,2

Equally: numbers n in whose factorial base representation A007623(n) there are prime-2 trailing zeros.

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

(define A232741 (MATCHING-POS 1 1 (lambda (n) (prime? (+ 1 (A055881 n))))))

Complement: A232742. Cf. A007623, A055881, A230403.

allocated

nonn

Antti Karttunen, Dec 01 2013

approved

editing

allocated for Antti Karttunen

allocated

approved