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

1,1

Links

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

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A194859 A194838 A085014 * A132283 A307081 A256440

Adjacent sequences: A082071 A082072 A082073 * A082075 A082076 A082077

Keyword

nonn

Author

Labos Elemer, Apr 07 2003

Status

approved