A299022 a(n) is the number of primes of the form 2*n - 1 + k!.

1, 3, 4, 1, 5, 3, 1, 6, 7, 1, 6, 1, 1, 6, 9, 0, 3, 11, 1, 9, 5, 1, 10, 2, 1, 9, 2, 1, 10, 9, 0, 3, 9, 1, 8, 9, 0, 5, 9, 1, 11, 1, 1, 8, 3, 0, 2, 10, 1, 10, 12, 1, 16, 12, 1, 10, 1, 0, 2, 2, 0, 3, 10, 1, 13, 3, 1, 14, 14, 0, 4, 1, 1, 16, 11, 0, 2, 12, 0, 4, 9, 1, 15, 3, 1, 10, 2, 1, 9, 8, 0, 1, 8, 1, 12, 9, 1, 10, 6

Offset

2,2

Comments

Records: 1, 3, 4, 5, 6, 7, 9, 11, 12, 16, 21, 22, 25, 26, ..., - Robert G. Wilson v, Mar 20 2018

When k >= 2*n-1, k! is a multiple of (2*n-1); then 2*n - 1 + k! is a multiple of (2*n-1) so it cannot be prime. - Michel Marcus, May 20 2018

Links

Robert G. Wilson v, Table of n, a(n) for n = 2..1500

Example

a(7)=3 because there are 3 primes of the form k!+13, i.e., 19 = 3!+13, 37 = 4!+13, 733 = 6!+13.

Mathematica

f[n_] := Block[{c = 0, k = 1, od = 2n -1}, While[k < od, If[PrimeQ[k! + od], c++]; k++]; c]; f@# & /@ Range[2, 100] (* Robert G. Wilson v, Mar 18 2018 *)

Prog

(PARI) a(n) = sum(k=2, 2*n-1, isprime(2*n - 1 + k!)); \\ Michel Marcus, May 19 2018

Crossrefs

Cf. A000040, A000142, A005408, A303733 (greedy inverse).

Sequence in context: A321624 A079529 A361508 * A298532 A133779 A137911

Adjacent sequences: A299019 A299020 A299021 * A299023 A299024 A299025

Keyword

easy,nonn

Author

G. L. Honaker, Jr., Mar 18 2018

Extensions

More terms from Robert G. Wilson v, Mar 18 2018

Status

approved