A080147 Positions of primes of the form 4*k+1 (A002144) among all primes (A000040).

3, 6, 7, 10, 12, 13, 16, 18, 21, 24, 25, 26, 29, 30, 33, 35, 37, 40, 42, 44, 45, 50, 51, 53, 55, 57, 59, 60, 62, 65, 66, 68, 70, 71, 74, 77, 78, 79, 80, 82, 84, 87, 88, 89, 97, 98, 100, 102, 104, 106, 108, 110, 112, 113, 116, 119, 121, 122, 123, 126, 127, 130, 134, 135

Offset: 1

Author

Antti Karttunen, Feb 11 2003

Keywords

• nonn
• easy

Comments

The asymptotic density of this sequence is 1/2 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

Examples

			7 is in the sequence because the 7th prime, 17, is of the form 4k+1.
4 is not in the sequence because the 4th prime, 7, is not of the form 4k+1.
		

Links

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

Crossrefs

Almost complement of A080148 (1 is excluded from both).

Cf. A000040, A002144.

Programs

Maple

with(numtheory,ithprime); pos_of_primes_k_mod_n(300,1,4);
pos_of_primes_k_mod_n := proc(upto_i,k,n) local i,a; a := []; for i from 1 to upto_i do if(k = (ithprime(i) mod n)) then a := [op(a),i]; fi; od; RETURN(a); end;
with(Bits): for n from 1 to 135 do if (And(ithprime(n),2)=0) then print(n) fi od; # Gary Detlefs, Dec 26 2011

Mathematica

Select[Range[135], Mod[Prime[#], 4] == 1 &] (* Amiram Eldar, Mar 01 2021 *)

PARI

k=0;forprime(p=2,1e4,k++;if(p%4==1,print1(k", "))) \\ Charles R Greathouse IV, Dec 27 2011

Formula

A002144(n) = A000040(a(n)).

Numbers k such that prime(k) AND 2 = 0. - Gary Detlefs, Dec 26 2011