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A174454 The smaller member p of a twin prime pair such that 5*p+6 is a square of a prime number. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 17 16:21 EST 2021. Contains 340246 sequences. (Running on oeis4.)