A098417 -id:A098417 - cp's OEIS frontend

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

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

nonn

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

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).

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.

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

Union of A022004 and A022005.

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

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

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

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

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

A098415 Greatest members r of prime triples (p,q,r) with p

Original entry on oeis.org

11, 13, 17, 19, 23, 43, 47, 73, 103, 107, 109, 113, 197, 199, 229, 233, 283, 313, 317, 353, 463, 467, 619, 647, 827, 829, 859, 863, 883, 887, 1093, 1097, 1283, 1303, 1307, 1429, 1433, 1453, 1487, 1489, 1493, 1613, 1669, 1699, 1789, 1873, 1877, 1879, 1999

Offset: 1

Reinhard Zumkeller, Sep 07 2004

nonn

Union of A098412 and A098413;

a(n)=A007529(n)+6; either a(n)=A098414(n)+2 or a(n)=A098414(n)+4.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Prime Triplet

Cf. A098424, A098416, A098417.

Transpose[Select[Partition[Prime[Range[350]],3,1],#[[3]]- #[[1]] == 6&]][[3]] (* Harvey P. Dale, Mar 17 2015 *)

is(n)=isprime(n) && isprime(n-6) && (isprime(n-2) || isprime(n-4)) \\ Charles R Greathouse IV, Feb 23 2017

A098416 (A007529(n) + A098415(n)) / 4.

Original entry on oeis.org

4, 5, 7, 8, 10, 20, 22, 35, 50, 52, 53, 55, 97, 98, 113, 115, 140, 155, 157, 175, 230, 232, 308, 322, 412, 413, 428, 430, 440, 442, 545, 547, 640, 650, 652, 713, 715, 725, 742, 743, 745, 805, 833, 848, 893, 935, 937, 938, 998, 1000, 1042, 1043, 1070, 1120, 1135

Offset: 1

Reinhard Zumkeller, Sep 07 2004

nonn

(A007529(n),2*a(n)+A098417(n), A098415(n)) is a prime triple (p,q,r) with p

Eric Weisstein's World of Mathematics, Prime Triplet

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

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A098415 Greatest members r of prime triples (p,q,r) with p

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A098416 (A007529(n) + A098415(n)) / 4.

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