

A330558


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


2



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
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OFFSET

0,7


LINKS

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


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


PROG

(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


CROSSREFS

Sequences related to the differences between successive primes: A001223 (Delta(p)), A028334, A080378, A104120, A330556A330561.
Sequence in context: A244160 A064099 A134021 * A237657 A244317 A130255
Adjacent sequences: A330555 A330556 A330557 * A330559 A330560 A330561


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Dec 29 2019


STATUS

approved



