A007529 - OEIS

A007529

Prime triples: p; p+2 or p+4; p+6 all prime.
(Formerly M3760)

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

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OFFSET

1,1

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.

FORMULA

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

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 *)

PROG

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

(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

CROSSREFS

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

Union of A022004 and A022005.

Sequence in context: A255229 A230217 A317250 * A287956 A266266 A246463

Adjacent sequences: A007526 A007527 A007528 * A007530 A007531 A007532

KEYWORD

nonn

AUTHOR

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

STATUS

approved