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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
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
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
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