A332733 a(n) is the smallest positive k such that n!*prime(n) + k is a prime.

1, 1, 1, 5, 1, 11, 11, 11, 1, 11, 23, 43, 19, 41, 17, 29, 1, 19, 71, 157, 1, 23, 79, 67, 47, 53, 37, 53, 31, 67, 73, 223, 307, 67, 1, 197, 151, 43, 43, 157, 89, 137, 47, 127, 173, 97, 89, 79, 223, 79, 83, 151, 163, 89, 167, 313, 179, 101, 127, 101, 181, 193, 421, 73

Offset

1,4

Comments

k equals nextprime(n!*prime(n)) - n!*prime(n).

Links

Table of n, a(n) for n=1..64.

Formula

a(n) = A151800(n!*prime(n)) - n!*prime(n).

Mathematica

spk[n_]:=Module[{c=n!Prime[n]}, NextPrime[c]-c]; Array[spk, 70] (* Harvey P. Dale, Aug 13 2021 *)

Prog

(PARI) a(n) = my(x=n!*prime(n)); nextprime(x+1) - x; \\ Michel Marcus, Feb 22 2020

Crossrefs

Cf. A000040, A000142, A151800, A332731.

Sequence in context: A159074 A147414 A117637 * A132000 A132001 A113261

Adjacent sequences: A332730 A332731 A332732 * A332734 A332735 A332736

Keyword

nonn

Author

Mohamed Sami Gattoufi, Feb 21 2020

Status

approved