A075408 Perfect powers pp such that pp+1 is prime.

1, 4, 16, 36, 100, 196, 256, 400, 576, 676, 1296, 1600, 2916, 3136, 4356, 5476, 7056, 8100, 8836, 12100, 13456, 14400, 15376, 15876, 16900, 17956, 21316, 22500, 24336, 25600, 28900, 30976, 32400, 33856, 41616, 42436, 44100, 50176, 52900, 55696

Offset

1,2

Comments

Of 1110 pp's < 10^6, 112 are such that pp+1 is prime and only seven are such that pp-1 is prime (see Mersenne primes (A000668)).

Links

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Formula

a(n) = A002496(n) - 1.

Example

pp=324900 is OK because pp=570^2 and pp+1=324901 (prime).

Mathematica

pp = Join[ Select[ Range[56000], Apply[GCD, Last[ Transpose[ FactorInteger[ # ]]]] > 1 & ]]; Select[pp, PrimeQ[ # + 1] & ]

Prog

(Python)
from sympy import isprime
print([n**2 for n in range(1, 240) if isprime(n**2 + 1)]) # Karl-Heinz Hofmann, Feb 02 2023

Crossrefs

Cf. A001597 (perfect powers), A072868 (pp-1 is prime).

Cf. A002496.

Sequence in context: A189145 A005722 A372635 * A206981 A318149 A233409

Adjacent sequences: A075405 A075406 A075407 * A075409 A075410 A075411

Keyword

easy,nonn

Author

Zak Seidov, Oct 11 2002

Extensions

Edited by Robert G. Wilson v, Oct 14 2002

Edited by N. J. A. Sloane, Dec 17 2009 at the suggestion of Rick Shepherd

Status

approved