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A375277
a(n) = n! (mod nextprime(n)).
1
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
0,3
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
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]
PROG
(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
CROSSREFS
Cf. A360825 (essentially the same).
Sequence in context: A362232 A138009 A131755 * A305812 A341857 A292403
KEYWORD
easy,nonn
AUTHOR
Robert G. Wilson v, Sep 18 2024
STATUS
approved