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 A080147 Positions of primes of the form 4*k+1 (A002144) among all primes (A000040). 10
 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 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

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Last modified November 26 10:15 EST 2022. Contains 358356 sequences. (Running on oeis4.)