A087293 Numbers k such that ((prime(k)*prime(k+1))^2 + 1)/2 is prime.

2, 3, 6, 14, 27, 30, 35, 37, 44, 55, 101, 106, 118, 127, 137, 140, 154, 172, 184, 233, 248, 256, 260, 289, 383, 389, 425, 461, 463, 485, 500, 503, 513, 552, 584, 610, 617, 630, 642, 696, 706, 714, 737, 746, 819, 884, 926, 952, 964, 978, 1004, 1008, 1019, 1027

Offset

1,1

Comments

Resulting primes are in A087294.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

2 is in the sequence because ((prime(2)*prime(3))^2 + 1)/2 = ((3*5)^2 + 1)/2 = 113 is prime.

Mathematica

Select[Range[1100], PrimeQ[((Prime[#]Prime[#+1])^2+1)/2]&] (* Harvey P. Dale, Mar 18 2022 *)

Crossrefs

Cf. A086893, A087294.

Sequence in context: A182756 A152092 A187033 * A250022 A240749 A331684

Adjacent sequences: A087290 A087291 A087292 * A087294 A087295 A087296

Keyword

nonn

Author

Ray Chandler, Aug 31 2003

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 06 2021

Status

approved