A082073 First difference set of primes with 4k+1 form: A002144.

8, 4, 12, 8, 4, 12, 8, 12, 16, 8, 4, 8, 4, 24, 12, 8, 16, 8, 12, 4, 32, 4, 8, 16, 12, 8, 4, 12, 20, 4, 20, 12, 4, 20, 16, 8, 4, 8, 12, 12, 16, 8, 4, 48, 12, 20, 16, 12, 8, 16, 8, 12, 4, 24, 12, 8, 12, 4, 24, 8, 24, 24, 4, 8, 4, 24, 12, 12, 8, 24, 4, 20, 4, 48, 8, 4, 12, 24, 20, 12, 4, 8, 12

Offset: 1

Author

Labos Elemer, Apr 07 2003

Keywords

• nonn
• easy

Comments

a(n) is divisible by 4, for all n.

Examples

			first and second 4k+1 primes are 5 and 13, so a(1)=13-5=8;
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002144, A002145, A082074, 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)]; ], {n, 1, 1000}]
Differences[Select[Prime[Range[200]],Mod[#,4]==1&]] (* Harvey P. Dale, Feb 05 2020 *)

PARI

p=5;forprime(q=7,1e3,if(q%4==1,print1(q-p", ");p=q)) \\ Charles R Greathouse IV, May 13 2012

Formula

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