

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
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OFFSET

1,2


COMMENTS

Of 1110 pp's < 10^6, 112 are such that pp+1 is prime and only seven are such that pp1 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 pp1 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



