A292411 a(n) = ((prime(n) - 1)/2)^2 modulo prime(n).

1, 4, 2, 3, 10, 13, 5, 6, 22, 8, 28, 31, 11, 12, 40, 15, 46, 17, 18, 55, 20, 21, 67, 73, 76, 26, 27, 82, 85, 32, 33, 103, 35, 112, 38, 118, 41, 42, 130, 45, 136, 48, 145, 148, 50, 53, 56, 57, 172, 175, 60, 181, 63, 193, 66, 202, 68, 208, 211, 71, 220, 77, 78, 235, 238, 83, 253, 87, 262

Offset: 2

Author

Alonso del Arte, Sep 16 2017

Keywords

• nonn
• easy

Comments

Also the square of (prime(n) - 1)/2 + 1 modulo prime(n).

Examples

			The fourth prime is 7; ((7 - 1)/2)^2 = 3^2 = 9 = 2 mod 7. Hence a(4) = 2.
The fifth prime is 11; ((11 - 1)/2)^2 = 5^2 = 25 = 3 mod 11. Hence a(5) = 3.
		

Crossrefs

Cf. A005097.

Programs

Mathematica

Table[PowerMod[(Prime[n] - 1)/2, 2, Prime[n]], {n, 2, 70}]

PARI

a(n) = lift(Mod((prime(n)-1)/2, prime(n))^2); \\ Michel Marcus, Sep 19 2017

Python

from sympy import prime
def A292411(n): return pow((p:=prime(n))-1>>1,2,p) # Chai Wah Wu, Feb 14 2025

Formula

a(n) = 4^(-1) mod prime(n). - R. J. Cintra, Jan 25 2025