A375277 a(n) = n! (mod nextprime(n)).

1, 1, 2, 1, 4, 1, 6, 2, 5, 1, 10, 1, 12, 3, 8, 1, 16, 1, 18, 4, 11, 1, 22, 22, 6, 5, 14, 1, 28, 1, 30, 33, 20, 31, 18, 1, 36, 7, 20, 1, 40, 1, 42, 8, 23, 1, 46, 19, 11, 9, 26, 1, 52, 30, 27, 10, 29, 1, 58, 1, 60, 43, 53, 56, 33, 1, 66, 12, 35, 1, 70, 1, 72, 27, 23, 66, 39, 1, 78

Offset: 0

Author

Robert G. Wilson v, Sep 18 2024

Keywords

• easy
• nonn

Comments

Same as A360825 except at n=3.

a(n) = 1 iff n+2 is prime (A040976).

a(n) = n iff n+1 is prime (A006093).

a(n) > n iff n is in A360805.

Links

• Dominic McCarty, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A360825 (essentially the same).

Cf. A000040, A000142, A006093, A040976, A360805.

Programs

Mathematica

a[n_] := Mod[n!, NextPrime[n]]; Array[a, 79, 0](* for large n *) a[n_] := Block[{m = NextPrime@ n, k = p = 1}, While[k < n +1, p = Mod[p*k, m]; k++]; p]

Python

from functools import reduce
from sympy import nextprime
def A375277(n): return ((p:=nextprime(n))-1)*pow(reduce(lambda i, j:i*j%p, range(n+1,p),1),-1,p)%p # Chai Wah Wu, Oct 18 2024