A174922 Lesser of twin primes p1 such that p1+(p2^2-p1^2) and p2+(p2^2-p1^2) are prime numbers.

5, 11, 29, 461, 599, 659, 809, 1019, 1289, 2027, 2141, 2309, 2339, 2801, 3329, 3557, 3581, 4127, 4421, 4547, 5879, 6761, 10091, 10457, 10709, 13829, 15329, 18911, 20231, 21839, 23561, 23909, 26249, 26879, 27581, 27689, 27917, 28109, 30491

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Keywords

• nonn

Comments

5+(7^2-5^2)=5+24=29; 7+(7^2-5^2)=7+24=31,..

Links

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

Crossrefs

Cf. A001359, A174913, A174915, A174916, A174917, A174920

Programs

Mathematica

lst={};Do[p1=Prime[n];p2=p1+2;If[PrimeQ[p2]&&PrimeQ[p1+(p2^2-p1^2)]&&PrimeQ[p2+(p2^2-p1^2)],AppendTo[lst,p1]],{n,8!}];lst
prQ[{a_,b_}]:=Module[{c=b^2-a^2},AllTrue[{a+c,b+c},PrimeQ]]; Transpose[ Select[ Select[ Partition[Prime[Range[5000]],2,1],#[[2]]-#[[1]] == 2&], prQ]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 12 2015 *)