|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
|