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

1,3

Links

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

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A097825 A002343 A371097 * A231516 A048793 A344084

Adjacent sequences: A082073 A082074 A082075 * A082077 A082078 A082079

Keyword

nonn

Author

Labos Elemer, Apr 07 2003

Status

approved