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

1,1

Comments

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

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A194184 A194217 A239971 * A378184 A244209 A156279

Adjacent sequences: A082070 A082071 A082072 * A082074 A082075 A082076

Keyword

nonn,easy

Author

Labos Elemer, Apr 07 2003

Status

approved