A060271 Difference between smallest prime following and largest prime preceding 2*(n-th prime).

2, 2, 4, 4, 4, 6, 6, 4, 4, 6, 6, 6, 4, 6, 8, 4, 14, 14, 6, 10, 10, 6, 4, 6, 4, 12, 12, 12, 12, 4, 6, 6, 6, 4, 14, 14, 4, 14, 6, 10, 6, 8, 4, 6, 8, 4, 10, 6, 8, 4, 4, 12, 8, 4, 12, 18, 18, 6, 10, 6, 6, 10, 4, 12, 12, 10, 12, 4, 10, 10, 8, 10, 6, 8, 4, 8, 14, 10, 12, 10, 10, 14, 4, 14, 4, 4, 20, 8

Offset

1,1

Links

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

Example

For n = 1: prime(1) = 2, 2*prime(1) = 4 is between 3 and 5, their difference is 2 = a(1).
For n = 6: prime(6) = 13, 2*prime(6) = 26 is between 23 and 29 and their difference is 6 = a(6).

Maple

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

Mathematica

dsplp[n_]:=Module[{np=2Prime[n]}, NextPrime[np]-NextPrime[np, -1]]; Array[ dsplp, 90] (* Harvey P. Dale, Mar 20 2013 *)

Prog

(PARI) a(n) = {my(m = 2*prime(n)); nextprime(m+1) - precprime(m-1); } \\ Amiram Eldar, Feb 08 2025

Crossrefs

Cf. A059786, A059787, A059788, A059789, A059790, A013633, A058043, A058249, A058044, A060267, A001223.

Sequence in context: A292264 A265263 A113320 * A085237 A279891 A110870

Adjacent sequences: A060268 A060269 A060270 * A060272 A060273 A060274

Keyword

nonn

Author

Labos Elemer, Mar 23 2001

Extensions

Offset changed to 1 and a(1) prepended by Amiram Eldar, Feb 08 2025

Status

approved