A046931 Prime islands: for n >= 2, a(n) = least prime whose adjacent primes are exactly 2n apart; a(1) = 3 by convention.

3, 5, 7, 29, 23, 53, 89, 223, 113, 331, 631, 211, 1381, 1129, 1637, 4759, 2579, 3433, 4297, 1327, 2179, 2503, 7993, 5623, 9587, 17257, 15859, 14107, 19609, 34981, 36433, 33247, 24281, 35617, 43331, 19661, 134513, 31397, 137029

Offset

1,1

Comments

For n > 1: (n) = A000040(A261525(n)+1) for n > 1. - Reinhard Zumkeller, Aug 23 2015

Links

T. D. Noe, Table of n, a(n) for n=1..100

Abhimanyu Kumar and Anuraag Saxena, Insulated primes, arXiv:2011.14210 [math.NT], 2020. Mentions this sequence.

Example

29 is in a sea of 6 composites, namely 24, 25, 26, 27, 28 and 30 and is the smallest such number, so a(4) = 29.

Mathematica

Join[{3}, Transpose[Flatten[Table[Select[Partition[Prime[Range[ 20000]], 3, 1], Last[#]-First[#]==2 n&, 1], {n, 2, 45}], 1]][[2]]] (* Harvey P. Dale, May 22 2012 *)

Crossrefs

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

Another version: see A098968 and A098969.

Cf. A031131. - Zak Seidov, Jan 25 2015

Cf. A261525, A000040.

Sequence in context: A288924 A093574 A076846 * A154551 A058047 A098860

Adjacent sequences: A046928 A046929 A046930 * A046932 A046933 A046934

Keyword

nonn,nice

Author

Marc LeBrun and David W. Wilson

Extensions

Typo in example fixed by Zak Seidov, Jan 25 2015

Status

approved