A005099 (( Primes == -1 (mod 4) ) + 1)/4.

1, 2, 3, 5, 6, 8, 11, 12, 15, 17, 18, 20, 21, 26, 27, 32, 33, 35, 38, 41, 42, 45, 48, 50, 53, 56, 57, 60, 63, 66, 68, 71, 77, 78, 83, 87, 90, 92, 95, 96, 105, 108, 110, 111, 116, 117, 120, 122, 123, 125, 126, 131, 137, 141, 143, 147, 150, 152, 155, 158, 161, 162, 165

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Numbers k such that 4*k - 1 is prime. - Michel Marcus, Dec 10 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Magma

[ (p+1)/4: p in PrimesUpTo(700) | p mod 4 eq 3 ]; // Klaus Brockhaus, Dec 22 2008

Mathematica

lst={};Do[p=4*n-1;If[PrimeQ[p], AppendTo[lst, n]], {n, 0, 10^3}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 10 2008 *)
(Select[Prime@ Range@ 120, Mod[#, 4] == 3 &] + 1)/4 (* or *) Select[Range@165, PrimeQ[4 # - 1] &] (* Michael De Vlieger, Dec 10 2015 *)

PARI

isok(n) = isprime(4*n-1); \\ Michel Marcus, Dec 10 2015

Formula

a(n) = (A002145(n) + 1)/4. - R. J. Mathar, Jun 07 2011

Extensions

More terms from Klaus Brockhaus, Dec 22 2008