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A160591 Indices of primes congruent to 5 modulo 12.

%I A160591 #23 Mar 18 2023 16:32:59
%S A160591 3,7,10,13,16,24,26,30,33,35,40,45,51,55,57,60,62,66,71,77,79,87,89,
%T A160591 97,98,102,104,108,113,116,119,123,126,135,137,139,140,142,148,152,
%U A160591 158,160,162,165,170,176,178,184,186,194,196,199,201,206,209,212,218,220,223
%N A160591 Indices of primes congruent to 5 modulo 12.
%C A160591 The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - _Amiram Eldar_, Mar 02 2021
%H A160591 Robert Israel, <a href="/A160591/b160591.txt">Table of n, a(n) for n = 1..10000</a>
%F A160591 a(n) = A000720(A040117(n)).
%e A160591 a(1) = 3 since the 3rd prime, A000040(3) = 5, is the first one to be equal to 5 (mod 12).
%e A160591 a(2) = 7 since the 7th prime, A000040(7) = 17, is the second one to be equal to 5 (mod 12).
%p A160591 res:= NULL: p:= 2:
%p A160591 for m from 2 to 1000 do
%p A160591   p:= nextprime(p);
%p A160591   if p mod 12 = 5 then res:= res, m fi;
%p A160591 od:
%p A160591 res; # _Robert Israel_, Dec 26 2016
%t A160591 Select[{#, Prime[#]}& /@ Range[500], Mod[#[[2]], 12] == 5&] [[All, 1]] (* _Jean-François Alcover_, Mar 23 2019 *)
%t A160591 Select[Range[300],Mod[Prime[#],12]==5&] (* _Harvey P. Dale_, Mar 18 2023 *)
%o A160591 (PARI) for(n=1,999, prime(n)%12==5 & print1(n","))
%Y A160591 A116602 lists the even terms of this sequence, divided by 2.
%Y A160591 Cf. A000720, A040117.
%K A160591 nonn
%O A160591 1,1
%A A160591 _M. F. Hasler_, May 21 2009