A059790 Distance between 2*(n-th prime) and nearest prime.

1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 1, 5, 5, 3, 3, 3, 1, 1, 1, 1, 3, 5, 3, 5, 1, 3, 1, 3, 1, 5, 5, 1, 5, 3, 1, 1, 3, 1, 3, 3, 1, 1, 3, 3, 1, 1, 1, 3, 1, 5, 3, 3, 1, 3, 1, 3, 1, 1, 3, 5, 3, 1, 1, 3, 3, 3, 1, 1, 3, 1, 3, 5, 3, 5, 3, 1, 3, 1, 3, 1, 1, 9, 3, 3, 3, 3, 5, 3, 1, 1, 3, 1, 3, 3, 5, 1, 3, 3, 9, 9

Offset: 1

Author

Labos Elemer, Feb 22 2001

Keywords

• nonn

Examples

			Distance 1 means that either 2p+1 or 2p-1 is also prime.
		

Links

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

Crossrefs

Cf. A005382, A005383, A005384, A005385.

Programs

Maple

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

Mathematica

a[n_] := Min@ Differences[{NextPrime[#, -1], #, NextPrime[#]} & @ (2*Prime[n])]; Array[a, 100]  (* Amiram Eldar, Feb 08 2025 *)

PARI

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

Extensions

Offset corrected by Amiram Eldar, Feb 08 2025