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

1,1

Comments

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

Links

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

Formula

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

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Cf. A000040, A002144.

Sequence in context: A189387 A091087 A138622 * A192593 A289009 A084463

Adjacent sequences: A080144 A080145 A080146 * A080148 A080149 A080150

Keyword

nonn,easy

Author

Antti Karttunen, Feb 11 2003

Status

approved