A226993 Primes p such that 2p - 1 and 2p + 1 are squarefree.

2, 3, 7, 11, 17, 19, 29, 43, 47, 53, 71, 79, 83, 89, 97, 101, 107, 109, 127, 151, 173, 179, 191, 197, 199, 223, 227, 233, 241, 251, 271, 277, 281, 307, 317, 331, 349, 353, 359, 379, 389, 397, 431, 439, 443, 449, 457, 461, 467, 479, 503, 521, 523, 547, 557, 569

Offset: 1

Author

Irina Gerasimova, Jun 26 2013

Keywords

• nonn

Examples

			3 is in the sequence because 3 is prime and both 2*3 - 1 = 5 and 2*3 + 1 = 7 are squarefree.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005117.

Programs

Maple

with(numtheory); P:=proc(q) local n; for n from 1 to q do
if isprime(n) then if issqrfree(2*n-1) and issqrfree(2*n+1) then print(n)
fi; fi; od; end: P(10^5); #Paolo P. Lava, Jun 26 2013

PARI

is(n)=isprime(n)&&issquarefree(2*n-1)&&issquarefree(2*n+1) \\ Charles R Greathouse IV, Jun 27 2013