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Lesser of twin primes p1 such that p1 + p2^2 - p1^2 is a prime number.
6

%I #9 Sep 11 2012 20:25:09

%S 3,5,11,17,29,71,101,281,311,419,461,521,599,617,641,659,809,827,857,

%T 881,1019,1061,1277,1289,1319,1607,1721,1949,2027,2111,2141,2309,2339,

%U 2381,2591,2729,2801,3329,3557,3581,3767,3851,4049,4127,4157,4217,4229

%N Lesser of twin primes p1 such that p1 + p2^2 - p1^2 is a prime number.

%C 3+(5^2-3^2)=3+16=19,..

%C Let x be the lesser of twin prime pairs. The sequence contains terms such that 5*x+4 is prime. - _Harvey P. Dale_, Sep 11 2012

%H Harvey P. Dale, <a href="/A174916/b174916.txt">Table of n, a(n) for n = 1..1000</a>

%t lst={}; Do[p1=Prime[n]; p2=p1+2; If[PrimeQ[p2] && PrimeQ[p1+(p2^2-p1^2)], AppendTo[lst, p1]], {n, 1000}]; lst

%t With[{ltp=Transpose[Select[Partition[Prime[Range[600]],2,1],#[[2]]- #[[1]]==2&]][[1]]}, Select[ltp,PrimeQ[5#+4]&]] (* _Harvey P. Dale_, Sep 11 2012 *)

%Y Cf. A001359, A174913, A174915.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Apr 02 2010