A073649 -id:A073649 - cp's OEIS frontend

A022005 Initial members of prime triples (p, p+4, p+6).

7, 13, 37, 67, 97, 103, 193, 223, 277, 307, 457, 613, 823, 853, 877, 1087, 1297, 1423, 1447, 1483, 1663, 1693, 1783, 1867, 1873, 1993, 2083, 2137, 2377, 2683, 2707, 2797, 3163, 3253, 3457, 3463, 3847, 4153, 4513, 4783, 5227, 5413, 5437, 5647, 5653, 5737, 6547

Offset: 1

Warut Roonguthai

Subsequence of A029710. - R. J. Mathar, May 06 2017

All terms are congruent to 1 (modulo 6). - Matt C. Anderson, May 22 2015

Matt C. Anderson, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe).
Tony Forbes and Norman Luhn, Prime k-tuplets.
Maxie D. Schmidt, New Congruences and Finite Difference Equations for Generalized Factorial Functions, arXiv:1701.04741 [math.CO], 2017.
Eric Weisstein's World of Mathematics, Prime Triplet.

Subsequence of A029710 and of A002476.
Subsequence of A007529.
Cf. A001359, A073649, A098413.

[p: p in PrimesUpTo(10000) | IsPrime(p+4) and IsPrime(p+6)]; // Vincenzo Librandi, Aug 23 2015

Select[Table[Prime[n], {n, 2000}], PrimeQ[# + 4] && PrimeQ[# + 6] &] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2011 *)

select(p->isprime(p+4) && isprime(p+6), primes(1000)) \\ Charles R Greathouse IV, Mar 17 2023

A073648 Middle members of prime triples {p, p+2, p+6}.

Original entry on oeis.org

7, 13, 19, 43, 103, 109, 193, 229, 313, 349, 463, 643, 823, 859, 883, 1093, 1279, 1303, 1429, 1483, 1489, 1609, 1873, 1999, 2083, 2239, 2269, 2659, 2689, 3253, 3463, 3529, 3673, 3919, 4003, 4129, 4519, 4639, 4789, 4933, 4969, 5233, 5479, 5503, 5653, 6199

Offset: 1

Amarnath Murthy, Aug 09 2002

Zak Seidov, Table of n,a(n) for n=1,2380, a(n)<2*10^6

Cf. A073649, A073650.

Cf. A098412, A098414.

Transpose[Select[Partition[Prime[Range[850]],3,1],Differences[#]=={2,4}&]][[2]]  (* Harvey P. Dale, Feb 20 2011 *)

a(n) = A022004(n) + 2.

More terms from Benoit Cloitre, Aug 13 2002

A098413 Greatest members p of prime triples (p-6, p-2, p).

Original entry on oeis.org

13, 19, 43, 73, 103, 109, 199, 229, 283, 313, 463, 619, 829, 859, 883, 1093, 1303, 1429, 1453, 1489, 1669, 1699, 1789, 1873, 1879, 1999, 2089, 2143, 2383, 2689, 2713, 2803, 3169, 3259, 3463, 3469, 3853, 4159, 4519, 4789, 5233, 5419, 5443, 5653, 5659, 5743

Offset: 1

Reinhard Zumkeller, Sep 07 2004

nonn

Subsequence of A046117; a(n) = A073649(n) + 2 = A022005(n) + 6.

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

Cf. A098412, A098415.

[p: p in PrimesUpTo(6500)|IsPrime(p) and IsPrime(p-6) and IsPrime(p-2)]; // Vincenzo Librandi, Dec 26 2010

Transpose[Select[Partition[Prime[Range[800]],3,1],Differences[#] == {4,2}&]][[3]] (* Harvey P. Dale, Aug 21 2013 *)

A073650 Define the composite field of a prime q to be f(q) = (t,s) if p, q, r are three consecutive primes and q-p = t and r-q = s. This is a sequence of primes q with field (2,6).

Original entry on oeis.org

31, 61, 73, 151, 271, 433, 571, 601, 1033, 1063, 1231, 1291, 1321, 1453, 1621, 2131, 2341, 2383, 2551, 2713, 2791, 3301, 3541, 4021, 4051, 4093, 4651, 4723, 5101, 5443, 5521, 5641, 5743, 5851, 6271, 6361, 6571, 6703, 6961, 7213, 8011, 9001, 9043, 9343

Offset: 1

Amarnath Murthy, Aug 09 2002

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Cf. A073648, A073649.

Transpose[Select[Partition[Prime[Range[1200]],3,1],Differences[#] == {2,6}&]][[2]] (* Harvey P. Dale, Jul 23 2011 *)

More terms from Benoit Cloitre, Aug 13 2002

A073651 Define the composite field of a prime q to be f(q) = (t,s) if p, q, r are three consecutive primes and q-p = t and r-q = s. This is a sequence of primes q with field (6,2).

Original entry on oeis.org

29, 59, 137, 179, 239, 269, 569, 599, 659, 1019, 1229, 1289, 1607, 1619, 2339, 2549, 2969, 3329, 3539, 3767, 3917, 3929, 4019, 4217, 4259, 4649, 4799, 5009, 5279, 5477, 5849, 5867, 6269, 6359, 6569, 6659, 6869, 7127, 7457, 7487, 7547, 7589, 8087, 8429, 8837, 8969, 9419, 9629

Offset: 1

Amarnath Murthy, Aug 09 2002

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Cf. A073648, A073649, A073650.

Transpose[Select[Partition[Prime[Range[1200]],3,1],Differences[#]=={6,2}&]][[2]] (* Harvey P. Dale, Jul 23 2011 *)

Corrected and extended by Ryan Propper, Jul 10 2005

Corrected and extended by Harvey P. Dale, Jul 23 2011

cp's OEIS Frontend

A022005 Initial members of prime triples (p, p+4, p+6).

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A073648 Middle members of prime triples {p, p+2, p+6}.

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A098413 Greatest members p of prime triples (p-6, p-2, p).

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A073650 Define the composite field of a prime q to be f(q) = (t,s) if p, q, r are three consecutive primes and q-p = t and r-q = s. This is a sequence of primes q with field (2,6).

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A073651 Define the composite field of a prime q to be f(q) = (t,s) if p, q, r are three consecutive primes and q-p = t and r-q = s. This is a sequence of primes q with field (6,2).

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Extensions