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

%I #11 Dec 24 2019 08:29:34

%S 71,191,6551,35447,79631,103391,207671,254927,264959,421079,479879,

%T 592367,700127,745751,949607,986567,1013399,1271087,1456919,1478591,

%U 1859279,2085287,2272727,2841071,5204039,5472671,6003887,6202751

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

%C Subsequence of A174370 and of A001359.

%H Amiram Eldar, <a href="/A174454/b174454.txt">Table of n, a(n) for n = 1..10000</a>

%e (71,73) are twin primes, and 5 * 71 + 6 = 19^2 is a square of a prime, which adds 71 to the sequence.

%e (9767,9769) are twin primes, 5 * 9767 + 6 = 221^2, but 221 = 13 * 17 is not prime, so 9767 is not in the sequence.

%t Select[Transpose[Select[Partition[Prime[Range[430000]],2,1], Last[#]- First[#] ==2&]][[1]],PrimeQ[Sqrt[5#+6]]&] (* _Harvey P. Dale_, Apr 22 2011 *)

%t Select[(Select[Range[5569], PrimeQ]^2 - 6)/5, And @@ PrimeQ[# + {0, 2}] &] (* _Amiram Eldar_, Dec 24 2019 *)

%Y Cf. A001359, A174370.

%K nonn

%O 1,1

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

%E Definition simplified, cross-references to unrelated sequences removed - _R. J. Mathar_, Nov 01 2010