A007529 Prime triples: p; p+2 or p+4; p+6 all prime.

5, 7, 11, 13, 17, 37, 41, 67, 97, 101, 103, 107, 191, 193, 223, 227, 277, 307, 311, 347, 457, 461, 613, 641, 821, 823, 853, 857, 877, 881, 1087, 1091, 1277, 1297, 1301, 1423, 1427, 1447, 1481, 1483, 1487, 1607, 1663, 1693, 1783, 1867, 1871, 1873, 1993, 1997

Offset: 1

Author

N. J. A. Sloane, Robert G. Wilson v

Keywords

• nonn

Comments

Or, prime(m) such that prime(m+2) = prime(m)+6. - Zak Seidov, May 07 2012

References

• H. Riesel, "Prime numbers and computer methods for factorization", Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, see p. 65.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000
• Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.

Crossrefs

Cf. A031924, A023201, A098414, A098415, A098424, A098416, A098417.

Union of A022004 and A022005.

Programs

Magma

[NthPrime(n): n in [1..310] | (NthPrime(n)+6) eq NthPrime(n+2)]; // Bruno Berselli, May 07 2012

Maple

N:= 10000: # to get all terms <= N
Primes:= select(isprime, [seq(2*i+1, i=1..floor((N+5)/2))]):locs:= select(t -> Primes[t+2]-Primes[t]=6, [$1..nops(Primes)-2]):
Primes[locs]; # Robert Israel, Apr 30 2015

Mathematica

ptrsQ[n_]:=PrimeQ[n+6]&&(PrimeQ[n+2]||PrimeQ[n+4])
Select[Prime[Range[400]],ptrsQ]  (* Harvey P. Dale, Mar 08 2011 *)

PARI

p=2;q=3;forprime(r=5,1e4,if(r-p==6,print1(p", "));p=q;q=r) \\ Charles R Greathouse IV, May 07 2012

Formula

a(n) = A098415(n) - 6. - Zak Seidov, Apr 30 2015