A023188 Lonely (or isolated) primes: least prime of distance n from nearest prime (n = 1 or even).

2, 5, 23, 53, 409, 293, 211, 1847, 3137, 2179, 3967, 23719, 16033, 40387, 44417, 24281, 158699, 220973, 172933, 321509, 38501, 58831, 203713, 268343, 206699, 829399, 824339, 413353, 2280767, 2305549, 3253631, 1272749, 2401807, 2844833, 3021241

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

a(1)=least prime of distance 1 from nearest prime.

if n>1 a(n)=least prime of distance 2n-2 from nearest prime.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..191 (first 65 terms from Daniel Lignon)
• Abhimanyu Kumar and Anuraag Saxena, Insulated primes, arXiv:2011.14210 [math.NT], 2020. Mentions this sequence. See also Notes Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 602-612.

Crossrefs

Related sequences: A023186-A023188, A046929-A046931, A051650, A051652, A051697-A051702, A051728-A051730.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = Table[0, {35}]; p = 2; q = 3; k = 1; Do[r = NextPrim[q]; m = Min[r - q, q - p]/2; If[m < 35 && a[[m]] == 0, a[[m]] = q]; p = q; q = r, {n, 1, 235000}]
Join[{2},Transpose[Flatten[Table[Select[Partition[Prime[ Range[ 1000000]],3,1], Min[ Differences[#]] == 2n&,1],{n,40}],1]][[2]]](* Harvey P. Dale, Nov 17 2013 *)

Extensions

a(36)-a(65) from Daniel Lignon, Aug 07 2015