A082074 One quarter of first differences of primes of the form 4*k+1 (A002144).

2, 1, 3, 2, 1, 3, 2, 3, 4, 2, 1, 2, 1, 6, 3, 2, 4, 2, 3, 1, 8, 1, 2, 4, 3, 2, 1, 3, 5, 1, 5, 3, 1, 5, 4, 2, 1, 2, 3, 3, 4, 2, 1, 12, 3, 5, 4, 3, 2, 4, 2, 3, 1, 6, 3, 2, 3, 1, 6, 2, 6, 6, 1, 2, 1, 6, 3, 3, 2, 6, 1, 5, 1, 12, 2, 1, 3, 6, 5, 3, 1, 2, 3, 4, 3, 2, 6, 1, 3, 2, 3, 6, 7, 3, 2, 3, 1, 3, 2, 3, 7, 3, 2, 1, 5

Offset: 1

Author

Labos Elemer, Apr 07 2003

Keywords

• nonn

Examples

			The first and second primes of the form 4*k+1 are 5 and 13, so a(1) = (13-5)/4 = 2.
		

Links

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

Crossrefs

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

Programs

Mathematica

k=0; m=4; r=1; 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[4*Range[1000]+1,PrimeQ]]/4 (* Harvey P. Dale, Dec 04 2011 *)

Formula

a(n) = (A002144(n+1) - A002144(n))/4.