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

Author

Felice Russo

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

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

Programs

Magma

[n: n in [1..2000] | IsPrime(4*n+1) and IsPrime(4*n-1)] // Vincenzo Librandi, Nov 18 2010

Mathematica

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

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

Extensions

More terms from Erich Friedman