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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
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).
Sequence in context: A189387 A091087 A138622 * A192593 A289009 A084463
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Feb 11 2003
STATUS
approved

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Last modified July 19 00:30 EDT 2024. Contains 374388 sequences. (Running on oeis4.)