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A330557
a(n) = number of primes p <= 2*n+1 with Delta(p) == 2 mod 4, where Delta(p) = nextprime(p) - p.
5
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, 12, 12, 12, 12, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 20, 21, 21
OFFSET
0,3
LINKS
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[2](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 2]: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: A020912 A194990 A231153 * A099199 A172474 A062276
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 29 2019
STATUS
approved