

A080147


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


11



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
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OFFSET

1,1


COMMENTS

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


LINKS



FORMULA

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



CROSSREFS

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


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



