A332731 a(n) is the smallest positive k such that n!*prime(n) - k is a prime.

1, 1, 1, 1, 11, 11, 1, 13, 1, 17, 1, 1, 53, 17, 1, 29, 23, 31, 23, 1, 29, 67, 31, 31, 43, 29, 181, 1, 83, 41, 101, 79, 179, 79, 43, 83, 47, 83, 163, 79, 53, 73, 59, 67, 347, 223, 67, 53, 97, 1, 157, 73, 1, 229, 101, 1, 263, 103, 101, 163, 139, 599, 103, 197, 73, 433, 313, 73

Offset

2,5

Comments

Equivalently, a(n) = n!*prime(n) minus the previous prime.

Links

Table of n, a(n) for n=2..69.

Formula

a(n) = n!*prime(n) - A007917(n!*prime(n)).

Example

For n=3, n!*prime(n) = 3!*prime(3) = 6*5 = 30, and the largest prime < 30 is 29, so a(3) = 30 - 29 = 1.

Mathematica

Table[With[{c=n!Prime[n]}, c-NextPrime[c, -1]], {n, 2, 70}] (* Harvey P. Dale, Sep 01 2024 *)

Prog

(PARI) a(n) = my(x=n!*prime(n)); x - precprime(x); \\ Michel Marcus, Feb 22 2020

Crossrefs

Cf. A000040, A000142, A007917, A332733.

Sequence in context: A287288 A287979 A268915 * A322270 A260589 A291367

Adjacent sequences: A332728 A332729 A332730 * A332732 A332733 A332734

Keyword

nonn

Author

Mohamed Sami Gattoufi, Feb 21 2020

Status

approved