A174454 The smaller member p of a twin prime pair such that 5*p+6 is a square of a prime number.

71, 191, 6551, 35447, 79631, 103391, 207671, 254927, 264959, 421079, 479879, 592367, 700127, 745751, 949607, 986567, 1013399, 1271087, 1456919, 1478591, 1859279, 2085287, 2272727, 2841071, 5204039, 5472671, 6003887, 6202751

Offset

1,1

Comments

Subsequence of A174370 and of A001359.

Links

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

Example

(71,73) are twin primes, and 5 * 71 + 6 = 19^2 is a square of a prime, which adds 71 to the sequence.
(9767,9769) are twin primes, 5 * 9767 + 6 = 221^2, but 221 = 13 * 17 is not prime, so 9767 is not in the sequence.

Mathematica

Select[Transpose[Select[Partition[Prime[Range[430000]], 2, 1], Last[#]- First[#] ==2&]][[1]], PrimeQ[Sqrt[5#+6]]&]  (* Harvey P. Dale, Apr 22 2011 *)
Select[(Select[Range[5569], PrimeQ]^2 - 6)/5, And @@ PrimeQ[# + {0, 2}] &] (* Amiram Eldar, Dec 24 2019 *)

Crossrefs

Cf. A001359, A174370.

Sequence in context: A140007 A023107 A174370 * A142808 A101110 A142893

Adjacent sequences: A174451 A174452 A174453 * A174455 A174456 A174457

Keyword

nonn

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 20 2010

Extensions

Definition simplified, cross-references to unrelated sequences removed - R. J. Mathar, Nov 01 2010

Status

approved