A060266 Difference between 2n and the following prime.

1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 5, 3, 1, 1, 5, 3, 1, 3, 1, 1, 3, 1, 5, 3, 1, 5, 3, 1, 1, 5, 3, 1, 3, 1, 1, 5, 3, 1, 3, 1, 5, 3, 1, 7, 5, 3, 1, 3, 1, 1, 3, 1, 1, 3, 1, 13, 11, 9, 7, 5, 3, 1, 3, 1, 5, 3, 1, 1, 9, 7, 5, 3, 1, 1, 5, 3, 1, 5, 3, 1, 3, 1, 5, 3, 1, 5, 3, 1, 1, 9, 7, 5, 3, 1, 1, 3, 1, 1, 11, 9, 7, 5

Offset: 1

Author

Labos Elemer, Mar 23 2001

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A020482, A049653, A060267, A060268, A060264.

Programs

Maple

with(numtheory): [seq(nextprime(2*i)-2*i,i=1..256)];

Mathematica

d2n[n_]:=Module[{c=2n},NextPrime[c]-c]; Array[d2n,120] (* Harvey P. Dale, May 14 2011 *)
Table[NextPrime@ # - # &[2 n], {n, 120}] (* Michael De Vlieger, Feb 18 2017 *)

PARI

a(n) = nextprime(2*n+1) - 2*n; \\ Michel Marcus, Feb 19 2017

Formula

Conjecture: Limit_{n->oo} (Sum_{k=1..n} a(k)) / (Sum_{k=1..n} log(2*k)) = 1. - Alain Rocchelli, Oct 24 2023