A379544 a(n) = ((p-1)^n + (p+1)^n) mod p^2, where p is the n-th prime.

0, 2, 5, 2, 110, 2, 238, 2, 414, 2, 682, 2, 1066, 2, 1410, 2, 2006, 2, 2546, 2, 3066, 2, 3818, 2, 4850, 2, 5562, 2, 6322, 2, 7874, 2, 9042, 2, 10430, 2, 11618, 2, 13026, 2, 14678, 2, 16426, 2, 17730, 2, 19834, 2, 22246, 2, 23766, 2, 25546, 2, 28270, 2, 30666

Offset

1,2

Links

Table of n, a(n) for n=1..57.

Project Euler, Problem 123, Prime Square Remainders

Example

For n = 3, prime(n) = 5, so a(3) = (5-1)^3 + (5+1)^3 mod 5^2 = 280 mod 25 = 5.

Mathematica

Table[p=Prime[n]; Mod[((p-1)^n+(p+1)^n), p^2], {n, 57}] (* James C. McMahon, Jan 07 2025 *)

Prog

(Python)
import sympy
def a(n):
  nth_prime = sympy.prime(n)
  nth_prime_sq = nth_prime**2
  return (pow(nth_prime-1, n, nth_prime_sq) + pow(nth_prime+1, n, nth_prime_sq)) % (nth_prime_sq)

Crossrefs

Sequence in context: A328264 A170908 A229029 * A055385 A160503 A108429

Adjacent sequences: A379541 A379542 A379543 * A379545 A379546 A379547

Keyword

nonn

Author

Do Thanh Nhan, Dec 24 2024

Status

approved