A174920 List of primes p1 such that (p1,p2) are twin primes where both 2*p1+p2 and p1+2*p2 are primes.

3, 5, 59, 269, 1949, 2999, 6359, 11489, 11549, 14549, 18539, 19889, 21839, 31079, 32909, 32969, 33329, 33599, 42569, 42839, 50459, 53549, 58109, 68879, 70199, 74609, 79229, 80909, 93809, 96329, 98909, 104309, 109139, 114599, 121019, 125789

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Keywords

• nonn

Comments

Terms >5 are congruent to 29 mod 30. - Zak Seidov, May 10 2012

Also 2*p1+p2 and p1+2*p2 are twin primes. - Zak Seidov, May 10 2012

Examples

			a(1)=3 because 3, 5 are twin primes and 2*3+5=11, 3+2*5=13 are also primes.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001359, A174913, A174915, A174916, A174917, A177335.

Cf. A132929, A177336.

Programs

Magma

[NthPrime(n): n in [1..12000] | forall{p: p in [NthPrime(n)+2,3*NthPrime(n)+2,3*NthPrime(n)+4] | IsPrime(p)}]; // Bruno Berselli, May 10 2012

Maple

select(q -> isprime(q) and isprime(q+2) and isprime(3*q+2) and isprime(3*q+4), [3,5,seq(i,i=29..200000,30)]); # Robert Israel, May 06 2019

Mathematica

lst={};Do[p1=Prime[n];p2=p1+2;If[PrimeQ[p2]&&PrimeQ[2*p1+p2]&&PrimeQ[p1+2*p2],AppendTo[lst,p1]],{n,8!}];lst

Formula

From Wesley Ivan Hurt, May 03 2022: (Start)

a(n) = A132929(n) - 1.

a(n) = A177336(n) - 2. (End)