A082076 First differences of primes of the form 4*k+3 (A002145), divided by 4.

1, 1, 2, 1, 2, 3, 1, 3, 2, 1, 2, 1, 5, 1, 5, 1, 2, 3, 3, 1, 3, 3, 2, 3, 3, 1, 3, 3, 3, 2, 3, 6, 1, 5, 4, 3, 2, 3, 1, 9, 3, 2, 1, 5, 1, 3, 2, 1, 2, 1, 5, 6, 4, 2, 4, 3, 2, 3, 3, 3, 1, 3, 6, 2, 7, 2, 3, 1, 2, 9, 6, 3, 1, 3, 5, 1, 5, 1, 5, 1, 2, 7, 5, 1, 3, 2, 7, 3, 2, 3, 3, 6, 1, 3, 5, 7, 3, 2, 4, 9, 2, 7, 5, 1, 2

Offset: 1

Author

Labos Elemer, Apr 07 2003

Keywords

• nonn

Examples

			The first and second primes of the form 4*k+3 are 3 and 7, so a(1) = (7-3)/4 = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002144, A002145, A082073, A082074, A082075.

Programs

Mathematica

k=0; m=4; r=3; Do[s=Mod[Prime[n], m]; If[Equal[s, r], rp=ep; k=k+1; ep=Prime[n]; Print[(ep-rp)/4]; ], {n, 1, 1000}]
Differences[Select[Prime[Range[400]],IntegerQ[(#-3)/4]&]]/4 (* Harvey P. Dale, Apr 29 2022 *)

Formula

a(n) = (A002145(n+1) - A002145(n))/4.