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

1,1

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

Links

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

Formula

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

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

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

Example

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

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

Prog

(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

Crossrefs

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

Cf. A132929, A177336.

Sequence in context: A106914 A337924 A049190 * A158314 A249011 A261533

Adjacent sequences: A174917 A174918 A174919 * A174921 A174922 A174923

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Status

approved