A174917 Lesser of twin primes p1 such that p2+(p2^2-p1^2) is a prime number.

5, 11, 29, 41, 107, 137, 149, 197, 239, 347, 431, 461, 569, 599, 659, 809, 821, 1019, 1229, 1289, 1481, 1619, 1787, 1877, 1931, 2027, 2129, 2141, 2309, 2339, 2657, 2687, 2801, 2969, 3119, 3329, 3467, 3557, 3581, 4001, 4019, 4127, 4241, 4421, 4547, 4649

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Keywords

• nonn

Comments

5+(7^2-5^2)=5+24=29,...

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001359, A174913, A174915, A174916

Programs

Mathematica

lst={};Do[p1=Prime[n];p2=p1+2;If[PrimeQ[p2]&&PrimeQ[p2+(p2^2-p1^2)],AppendTo[lst,p1]],{n,4*6!}];lst
Select[Partition[Prime[Range[700]],2,1],#[[2]]-#[[1]]==2&& PrimeQ[ #[[2]]+ #[[2]]^2-#[[1]]^2]&][[All,1]] (* Harvey P. Dale, Dec 18 2021 *)