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

1,1

Links

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

Example

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

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

Prog

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

Crossrefs

Cf. A005117.

Sequence in context: A040103 A045323 A161185 * A235482 A375818 A155141

Adjacent sequences: A226990 A226991 A226992 * A226994 A226995 A226996

Keyword

nonn

Author

Irina Gerasimova, Jun 26 2013

Status

approved