cp's OEIS Frontend

A330557 a(n) = number of primes p <= 2*n+1 with Delta(p) == 2 mod 4, where Delta(p) = nextprime(p) - p.

%I A330557 #16 Sep 08 2022 08:46:24
%S A330557 0,1,2,2,2,3,3,3,4,4,4,5,5,5,6,7,7,7,7,7,8,8,8,9,9,9,10,10,10,11,12,
%T A330557 12,12,12,12,13,14,14,14,14,14,15,15,15,15,15,15,15,15,15,16,16,16,17,
%U A330557 17,17,18,18,18,18,18,18,18,18,18,19,19,19,20,21,21
%N A330557 a(n) = number of primes p <= 2*n+1 with Delta(p) == 2 mod 4, where Delta(p) = nextprime(p) - p.
%H A330557 Robert Israel, <a href="/A330557/b330557.txt">Table of n, a(n) for n = 0..10000</a>
%p A330557 N:= 100: # for a(0)..a(N)
%p A330557 P:= select(isprime, [seq(i,i=3..nextprime(2*N+1),2)]):
%p A330557 Delta:= P[2..-1]-P[1..-2] mod 4:
%p A330557 A:= Array(0..N): t:= 0: j:= 1:
%p A330557 for n from 0 to N do
%p A330557   m:= 2*n+1:
%p A330557   if m = P[j] then t:= t + charfcn[2](Delta[j]); j:= j+1 fi;
%p A330557   A[n]:= t
%p A330557 od:
%p A330557 convert(A,list); # _Robert Israel_, Dec 31 2019
%o A330557 (Magma) [#[p:p in PrimesInInterval(1,2*n+1)| (NextPrime(p)-p) mod 4 eq 2]:n in [0..80]]; // _Marius A. Burtea_, Dec 31 2019
%Y A330557 Sequences related to the differences between successive primes: A001223 (Delta(p)), A028334, A080378, A104120, A330556-A330561.
%K A330557 nonn
%O A330557 0,3
%A A330557 _N. J. A. Sloane_, Dec 29 2019