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A330558 a(n) = number of primes p <= 2*n+1 with Delta(p) == 0 mod 4, where Delta(p) = nextprime(p) - p.

%I A330558 #14 Sep 08 2022 08:46:24
%S A330558 0,0,0,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,
%T A330558 6,6,6,6,6,7,7,7,7,7,8,8,8,8,9,9,9,10,10,10,11,11,11,11,11,11,11,11,
%U A330558 11,12,12,12,12,12,12,12,12,12,12,12,12,12,12
%N A330558 a(n) = number of primes p <= 2*n+1 with Delta(p) == 0 mod 4, where Delta(p) = nextprime(p) - p.
%H A330558 Robert Israel, <a href="/A330558/b330558.txt">Table of n, a(n) for n = 0..10000</a>
%p A330558 N:= 100: # for a(0)..a(N)
%p A330558 P:= select(isprime, [seq(i,i=3..nextprime(2*N+1),2)]):
%p A330558 Delta:= P[2..-1]-P[1..-2] mod 4:
%p A330558 A:= Array(0..N): t:= 0: j:= 1:
%p A330558 for n from 0 to N do
%p A330558 m:= 2*n+1:
%p A330558 if m = P[j] then t:= t + charfcn[0](Delta[j]); j:= j+1 fi;
%p A330558 A[n]:= t
%p A330558 od:
%p A330558 convert(A,list); # _Robert Israel_, Dec 31 2019
%o A330558 (Magma) [#[p:p in PrimesInInterval(1,2*n+1)| (NextPrime(p)-p) mod 4 eq 0]:n in [0..80]]; // _Marius A. Burtea_, Dec 31 2019
%Y A330558 Sequences related to the differences between successive primes: A001223 (Delta(p)), A028334, A080378, A104120, A330556-A330561.
%K A330558 nonn
%O A330558 0,7
%A A330558 _N. J. A. Sloane_, Dec 29 2019