A059790 - OEIS

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

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OFFSET

1,6

LINKS

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

EXAMPLE

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

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 *)

PROG