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

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, 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, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12

Offset: 0

Author

N. J. A. Sloane, Dec 29 2019

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Sequences related to the differences between successive primes: A001223 (Delta(p)), A028334, A080378, A104120, A330556-A330561.

Programs

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

Maple

N:= 100: # for a(0)..a(N)
P:= select(isprime, [seq(i,i=3..nextprime(2*N+1),2)]):
Delta:= P[2..-1]-P[1..-2] mod 4:
A:= Array(0..N): t:= 0: j:= 1:
for n from 0 to N do
m:= 2*n+1:
if m = P[j] then t:= t + charfcn[0](Delta[j]); j:= j+1 fi;
A[n]:= t
od:
convert(A,list); # Robert Israel, Dec 31 2019