A104197 Largest nonnegative integer r such that prime(n) + r and prime(n) - r are both prime.

0, 0, 2, 4, 8, 10, 14, 12, 20, 24, 28, 34, 38, 40, 42, 50, 54, 48, 64, 68, 66, 72, 80, 84, 94, 98, 96, 104, 102, 110, 124, 126, 134, 132, 144, 132, 154, 150, 164, 144, 174, 178, 188, 190, 192, 180, 208, 220, 222, 210, 230, 228, 238, 248, 252, 260, 252, 252, 270

Offset

1,3

Comments

a(n) can be thought of as the radius of the largest 1-dimensional circle centered at prime(n) and consisting entirely of primes.

Links

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

Example

r = 4 is the largest nonnegative integer r such that prime(4) + 4 = 11 and prime(4) - 4 = 3 are both prime; so a(4) = 4.

Mathematica

a[p_] := Module[{k = p-3}, While[!PrimeQ[p+k] || !PrimeQ[p-k], k-=2]; k]; Join[{0}, a/@Select[Range[3, 1000], PrimeQ]] (* Amiram Eldar, Mar 24 2019 *)

Crossrefs

Sequence in context: A190751 A030232 A102024 * A323440 A350804 A285626

Adjacent sequences: A104194 A104195 A104196 * A104198 A104199 A104200

Keyword

easy,nonn

Author

Joseph L. Pe, Mar 12 2005

Status

approved