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A080148 Positions of primes of the form 4*k+3 (A002145) among all primes (A000040).

%I A080148 #49 Mar 02 2021 06:00:05
%S A080148 2,4,5,8,9,11,14,15,17,19,20,22,23,27,28,31,32,34,36,38,39,41,43,46,
%T A080148 47,48,49,52,54,56,58,61,63,64,67,69,72,73,75,76,81,83,85,86,90,91,92,
%U A080148 93,94,95,96,99,101,103,105,107,109,111,114,115,117,118,120,124,125,128
%N A080148 Positions of primes of the form 4*k+3 (A002145) among all primes (A000040).
%C A080148 It appears that a(n) = k such that binomial(prime(k),3) mod 2 = 1. See Maple code. - _Gary Detlefs_, Dec 06 2011
%C A080148 The above is correct (work mod 4). - _Charles R Greathouse IV_, Dec 06 2011
%C A080148 The asymptotic density of this sequence is 1/2 (by Dirichlet's theorem). - _Amiram Eldar_, Mar 01 2021
%H A080148 Zak Seidov, <a href="/A080148/b080148.txt">Table of n, a(n) for n = 1..10000</a>
%F A080148 a(n) = A049084(A002145(n)). - _R. J. Mathar_, Oct 06 2008
%p A080148 pos_of_primes_k_mod_n(300,3,4); # Given in A080147.
%p A080148 A080148 := proc(n)
%p A080148         numtheory[pi](A002145(n)) ;
%p A080148 end proc:
%p A080148 seq(A080148(n),n=1..40) ; # _R. J. Mathar_, Dec 08 2011
%t A080148 Flatten[Position[Prime[Range[200]],_?(IntegerQ[(#-3)/4]&)]] (* _Harvey P. Dale_, Jun 06 2011 *)
%t A080148 Select[Range[135], Mod[Prime[#], 4] == 3 &] (* _Amiram Eldar_, Mar 01 2021 *)
%o A080148 (PARI) i=0;forprime(p=2,1e3,i++;if(p%4==3,print1(i", "))) \\ _Charles R Greathouse IV_, Dec 06 2011
%Y A080148 Almost complement of A080147 (1 is excluded from both).
%Y A080148 Cf. A000040, A002145, A049084.
%K A080148 nonn
%O A080148 1,1
%A A080148 _Antti Karttunen_, Feb 11 2003