A082075 First differences of primes of the form 4*k+3 (A002145).

4, 4, 8, 4, 8, 12, 4, 12, 8, 4, 8, 4, 20, 4, 20, 4, 8, 12, 12, 4, 12, 12, 8, 12, 12, 4, 12, 12, 12, 8, 12, 24, 4, 20, 16, 12, 8, 12, 4, 36, 12, 8, 4, 20, 4, 12, 8, 4, 8, 4, 20, 24, 16, 8, 16, 12, 8, 12, 12, 12, 4, 12, 24, 8, 28, 8, 12, 4, 8, 36, 24, 12, 4, 12, 20, 4, 20, 4, 20, 4, 8, 28, 20, 4

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.
		

Links

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

Crossrefs

Cf. A002144, A002145, A082073, A082074, A082075, A082076.

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]; ], {n, 1, 1000}]

Formula

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