A174916 Lesser of twin primes p1 such that p1 + p2^2 - p1^2 is a prime number.

3, 5, 11, 17, 29, 71, 101, 281, 311, 419, 461, 521, 599, 617, 641, 659, 809, 827, 857, 881, 1019, 1061, 1277, 1289, 1319, 1607, 1721, 1949, 2027, 2111, 2141, 2309, 2339, 2381, 2591, 2729, 2801, 3329, 3557, 3581, 3767, 3851, 4049, 4127, 4157, 4217, 4229

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Keywords

• nonn

Comments

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

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

Links

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

Crossrefs

Cf. A001359, A174913, A174915.

Programs

Mathematica

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