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A075408 Perfect powers pp such that pp+1 is prime. 0
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

Table of n, a(n) for n=1..40.

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] & ]

CROSSREFS

Cf. A001597: perfect powers, m^k where m is an integer and k >= 2.

Cf. A072868: perfect powers pp such that pp-1 is prime.

Sequence in context: A207436 A189145 A005722 * 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 June 22 20:39 EDT 2021. Contains 345389 sequences. (Running on oeis4.)