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
Keywords
Examples
(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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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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 *)
Extensions
Definition simplified, cross-references to unrelated sequences removed - R. J. Mathar, Nov 01 2010
Comments