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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. 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 (list; graph; refs; listen; history; text; internal format)
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, A330556-A330561.

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

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Last modified June 22 20:16 EDT 2021. Contains 345388 sequences. (Running on oeis4.)