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

1,4

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A049653 A281680 A377864 * A073310 A174414 A046929

Adjacent sequences: A060263 A060264 A060265 * A060267 A060268 A060269

Keyword

nonn

Author

Labos Elemer, Mar 23 2001

Status

approved