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 A075408 Perfect powers pp such that pp+1 is prime. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 10 07:40 EDT 2024. Contains 375773 sequences. (Running on oeis4.)