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

2,2

Comments

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

Links

Table of n, a(n) for n=2..70.

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A005097.

Sequence in context: A026177 A026196 A026216 * A069547 A282772 A227041

Adjacent sequences: A292408 A292409 A292410 * A292412 A292413 A292414

Keyword

nonn,easy

Author

Alonso del Arte, Sep 16 2017

Status

approved