A045753 Numbers n such that 4n-1 and 4n+1 are both primes.

1, 3, 15, 18, 27, 45, 48, 57, 60, 78, 87, 105, 108, 150, 165, 207, 255, 258, 273, 288, 330, 357, 363, 372, 402, 405, 417, 447, 468, 483, 507, 522, 528, 567, 585, 648, 672, 678, 750, 780, 792, 813, 825, 840, 843, 867, 882, 885, 918, 942, 963, 1005, 1023

Offset

1,2

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Example

3 belongs to the sequence because 4*3+1 and 4*3-1 are both primes.

Mathematica

Select[Range[1023], And @@ PrimeQ[{-1, 1} + 4# ] &] (* Ray Chandler, Dec 06 2006 *)

Prog

(Magma) [n: n in [1..2000] | IsPrime(4*n+1) and IsPrime(4*n-1)] // Vincenzo Librandi, Nov 18 2010
(PARI) list(lim)=my(v=List(), p=2); forprime(q=3, 4*lim+1, if(q-p==2 && p%4==3, listput(v, q\4)); p=q); Vec(v) \\ Charles R Greathouse IV, Dec 03 2016

Crossrefs

Cf. A040040, A002822, A124065, A124518-A124522, A063983.

Sequence in context: A077225 A236526 A039559 * A022381 A206367 A039570

Adjacent sequences: A045750 A045751 A045752 * A045754 A045755 A045756

Keyword

nonn,easy

Author

Felice Russo

Extensions

More terms from Erich Friedman

Status

approved