A380421 a(n) is the inverse of 2^3 modulo prime(n).

2, 2, 1, 7, 5, 15, 12, 3, 11, 4, 14, 36, 27, 6, 20, 37, 23, 42, 9, 64, 10, 52, 78, 85, 38, 13, 67, 41, 99, 16, 82, 120, 87, 56, 19, 59, 102, 21, 65, 112, 68, 24, 169, 74, 25, 132, 28, 142, 86, 204, 30, 211, 157, 225, 33, 101, 34, 104, 246, 177, 110, 192, 39, 274

Offset: 2

Author

R. J. Cintra, Jan 25 2025

Keywords

• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A006254, A292411.

Programs

Maple

seq(1/8 mod ithprime(n), n=2..65);  # Alois P. Heinz, Feb 14 2025

Mathematica

a[n_] := ModularInverse[8, Prime[n]]; Array[a, 100, 2] (* Amiram Eldar, Feb 05 2025 *)

PARI

a(n) = lift(1/Mod(8, prime(n))); \\ Michel Marcus, Jan 25 2025

Python

from sympy import prime
def A380421(n): return pow(8,-1,prime(n)) # Chai Wah Wu, Feb 14 2025

Formula

a(n) = 8^(-1) (mod prime(n)) for n >= 2.

a(n) = (A006254(n) * A292411(n)) (mod prime(n)) for n >= 2.

If prime(n) mod 8 = j in {1, 3, 5, 7}, then a(n) = (1 + (8-j)*prime(n))/8. - Robert Israel, Feb 24 2025