A174913 Lesser of twin primes p1 and p2 such that 2*p1+p2 is a prime number.

3, 5, 17, 29, 59, 149, 197, 227, 239, 269, 419, 569, 659, 1277, 1427, 1487, 1667, 1949, 2087, 2129, 2267, 2339, 2549, 2789, 2999, 3359, 3389, 3929, 4049, 4157, 4217, 4229, 4517, 4637, 5099, 5417, 5477, 6089, 6197, 6299, 6359, 6569, 6659, 6827, 6959, 7127

Offset

1,1

Comments

(p1, p2=p1+2) is a pair of twin primes.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Maple

select(t -> isprime(t) and isprime(t+2) and isprime(3*t+2), [3, seq(i, i=5..10000, 6)]); # Robert Israel, Dec 07 2025

Mathematica

lst={}; Do[p1=Prime[n]; p2=p1+2; If[PrimeQ[p2]&&PrimeQ[2*p1+p2], AppendTo[lst, p1]], {n, 7!}]; lst
Transpose[Select[Partition[Prime[Range[1000]], 2, 1], #[[2]]-#[[1]] == 2 && PrimeQ[ 2#[[1]]+ #[[2]]]&]][[1]] (* Harvey P. Dale, Apr 09 2012 *)

Prog

(Python)
from itertools import islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    p1, p2 = 3, 5
    while True:
        if p2-p1 == 2 and isprime(2*p1+p2): yield p1
        p1, p2 = p2, nextprime(p2)
print(list(islice(agen(), 46))) # Michael S. Branicky, Dec 07 2025
(PARI) isok(p) = isprime(p)&&isprime(p+2)&&isprime(2*p+(p+2)); \\ Bruce Nye, Apr 09 2026

Crossrefs

Cf. A001359

Sequence in context: A023226 A113169 A350856 * A079496 A230639 A038898

Adjacent sequences: A174910 A174911 A174912 * A174914 A174915 A174916

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Extensions

Definition edited by Harvey P. Dale, Aug 13 2024

Status

approved