A093012 Numbers k such that prime(k) == 3 (mod 16).

2, 8, 19, 23, 32, 38, 41, 47, 49, 63, 81, 91, 95, 101, 103, 117, 120, 125, 131, 138, 153, 161, 182, 188, 193, 195, 208, 225, 232, 241, 248, 256, 262, 266, 272, 280, 292, 300, 304, 314, 317, 321, 327, 334, 346, 351, 365, 370, 376, 385, 394, 409, 410, 414, 427

Offset: 1

Author

Ray Chandler, Mar 15 2004, revised Nov 06 2006

Keywords

• nonn

Comments

A091968 indexed by A000040.

The asymptotic density of this sequence is 1/8 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000040, A000720, A091968, A092022.

Programs

Magma

[n: n in [1..450]|(NthPrime(n) mod 16) eq 3] // G. C. Greubel, Feb 05 2019

Mathematica

Select[Range[430], Mod[Prime[ # ], 16] == 3 &] (* Ray Chandler, Nov 06 2006 *)

PARI

{isok(n) = Mod(prime(n), 16)==3};
for(n=1, 450, if(isok(n)==1, print1(n, ", "), 0)) \\ G. C. Greubel, Feb 05 2019

Formula

A000040(a(n)) = A091968(n).

a(n) = A000720(A091968(n)).