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%I #19 Feb 03 2023 08:18:32
%S 1,4,16,36,100,196,256,400,576,676,1296,1600,2916,3136,4356,5476,7056,
%T 8100,8836,12100,13456,14400,15376,15876,16900,17956,21316,22500,
%U 24336,25600,28900,30976,32400,33856,41616,42436,44100,50176,52900,55696
%N Perfect powers pp such that pp+1 is prime.
%C 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)).
%H Karl-Heinz Hofmann, <a href="/A075408/b075408.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A002496(n) - 1.
%e pp=324900 is OK because pp=570^2 and pp+1=324901 (prime).
%t pp = Join[ Select[ Range[56000], Apply[GCD, Last[ Transpose[ FactorInteger[ # ]]]] > 1 & ]]; Select[pp, PrimeQ[ # + 1] & ]
%o (Python)
%o from sympy import isprime
%o print([n**2 for n in range(1,240) if isprime(n**2 + 1)]) # _Karl-Heinz Hofmann_, Feb 02 2023
%Y Cf. A001597 (perfect powers), A072868 (pp-1 is prime).
%Y Cf. A002496.
%K easy,nonn
%O 1,2
%A _Zak Seidov_, Oct 11 2002
%E Edited by _Robert G. Wilson v_, Oct 14 2002
%E Edited by _N. J. A. Sloane_, Dec 17 2009 at the suggestion of Rick Shepherd