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

%I A080147 #27 Sep 20 2022 09:31:22
%S A080147 3,6,7,10,12,13,16,18,21,24,25,26,29,30,33,35,37,40,42,44,45,50,51,53,
%T A080147 55,57,59,60,62,65,66,68,70,71,74,77,78,79,80,82,84,87,88,89,97,98,
%U A080147 100,102,104,106,108,110,112,113,116,119,121,122,123,126,127,130,134,135
%N A080147 Positions of primes of the form 4*k+1 (A002144) among all primes (A000040).
%C A080147 The asymptotic density of this sequence is 1/2 (by Dirichlet's theorem). - _Amiram Eldar_, Mar 01 2021
%H A080147 Zak Seidov, <a href="/A080147/b080147.txt">Table of n, a(n) for n = 1..10000</a>
%F A080147 A002144(n) = A000040(a(n)).
%F A080147 Numbers k such that prime(k) AND 2 = 0. - _Gary Detlefs_, Dec 26 2011
%e A080147 7 is in the sequence because the 7th prime, 17, is of the form 4k+1.
%e A080147 4 is not in the sequence because the 4th prime, 7, is not of the form 4k+1.
%p A080147 with(numtheory,ithprime); pos_of_primes_k_mod_n(300,1,4);
%p A080147 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;
%p A080147 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
%t A080147 Select[Range[135], Mod[Prime[#], 4] == 1 &] (* _Amiram Eldar_, Mar 01 2021 *)
%o A080147 (PARI) k=0;forprime(p=2,1e4,k++;if(p%4==1,print1(k", "))) \\ _Charles R Greathouse IV_, Dec 27 2011
%Y A080147 Almost complement of A080148 (1 is excluded from both).
%Y A080147 Cf. A000040, A002144.
%K A080147 nonn,easy
%O A080147 1,1
%A A080147 _Antti Karttunen_, Feb 11 2003