A232741 - OEIS

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A232741

Numbers n for which 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

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OFFSET

1,2

COMMENTS

Numbers n for which A055881(n) is one of the terms of A006093.

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

The sequence can be described 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.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8748

PROG

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

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

CROSSREFS

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

Sequence in context: A083210 A345913 A187392 * A108120 A108586 A184522

Adjacent sequences: A232738 A232739 A232740 * A232742 A232743 A232744

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 01 2013

STATUS

approved