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A096453 Primes p such that the number of primes q, 5 <= q < p, congruent to 1 mod 3, is two less than the number of such primes congruent to 2 mod 3.

%I A096453 #20 Aug 09 2025 01:43:18
%S A096453 31,59,67,73,97,103,109,127,137,149,157,179,191,197,211,241,257,347,
%T A096453 353,379,389,401,419,431,439,449,461,467,761,773,797,1787,1801,1823,
%U A096453 1847,1867,1873,1879,1901,3761,9203,198479,198593,608981812531,608981812651,608981812697
%N A096453 Primes p such that the number of primes q, 5 <= q < p, congruent to 1 mod 3, is two less than the number of such primes congruent to 2 mod 3.
%H A096453 Andrew Howroyd, <a href="/A096453/b096453.txt">Table of n, a(n) for n = 1..1000</a>
%p A096453 ct := -2: q:=2: for n from 2 to 20000 do p:=q: q:=ithprime(n): ct:=ct+`if`(p mod 3 = 1, -1, 1): if(ct=2)then printf("%d, ", q): fi: od: # _Nathaniel Johnston_, Jun 16 2011
%t A096453 npc1Q[n_]:=Module[{tot=PrimePi[n]-3,c},c=Count[Prime[Range[3,tot+2]],_?(Mod[ #,3]==1&)];c==tot/2-1]; Select[Prime[Range[18000]],npc1Q] (* _Harvey P. Dale_, Aug 22 2013 *)
%o A096453 (PARI) lista(limit=10^6)={my(c=2); forprime(p=5, limit, if(!c, print1(p, ", ")); if(p%3==1, c++, c--))} \\ _Andrew Howroyd_, Aug 09 2025
%Y A096453 Cf. A096447-A096455.
%K A096453 nonn
%O A096453 1,1
%A A096453 _Yasutoshi Kohmoto_, Aug 12 2004
%E A096453 More terms and better definition from _Joshua Zucker_, May 21 2006
%E A096453 a(44) onwards from _Andrew Howroyd_, Aug 09 2025