A061671 -id:A061671 - cp's OEIS frontend

A083409 Number of prime k-tuplet constellations, i.e., patterns with minimal diameter A008407.

1, 2, 1, 2, 1, 2, 3, 4, 2, 2, 2, 6, 2, 4, 2, 4, 2, 4, 2, 2, 4, 2, 4, 18, 2, 8, 10, 2, 2, 2, 4, 14, 20, 2, 2, 2, 6, 26, 26, 8, 2, 6, 18, 4, 4, 4, 2, 2, 22, 22, 2, 2, 26, 6, 6, 2, 2, 4, 2, 2, 6, 2, 2, 2, 2, 18, 2, 20, 2, 2, 2, 10, 2, 14, 14, 40, 8, 2, 14, 14, 16, 4, 2, 2, 60, 50, 2, 2, 2, 16, 2, 18, 12

Offset: 2

Frank Ellermann, Jun 07 2003

nonn

			For a(8) = 3 octuplet patterns see A065706. for a(6) = 1 sextet see A061671.

T. D. Noe, Table of n, a(n) for n=2..305 (from Engelsma's data)
Thomas J Engelsma, Permissible Patterns.
Tony Forbes and Norman Luhn, Patterns of prime k-tuplets & the Hardy-Littlewood constants.
Eric Weisstein's World of Mathematics, k-Tuple Conjecture.

Cf. A008407, A020497, A023193, A061671, A065688, A065706.

More terms from Engelsma's website sent by T. D. Noe, Jul 21 2006

A066081 a(n) = smallest m such that m+2^j and m-2^j are prime for all 0 < j <= n.

Original entry on oeis.org

5, 9, 15, 50943795, 40874929095, 616517522595975, 93487500801880185, 64606701602327559675

Offset: 1

Frank Ellermann, Dec 03 2001

Is this sequence infinite?

			9-4, 9-2, 9+2, 9+4 are prime, but not 5+4 = 7+2, therefore a(2) = 9.

Felice Russo, Prime puzzle 167.
Marek Wolf, Conjectures on the gaps between consecutive primes

Prime quadruples: A014561, sextets: A061671, octets: A066082.

a(5) and a(6) from Don Reble, Dec 07 2001

a(7) from Jim Fougeron (Feb 07) confirmed by Phil Carmody, who also found a(8) (Feb 14 2002).

A066082 Prime octets: numbers k such that 210*k - 105 +- 2^j are prime for all 1 <= j <= 4.

Original entry on oeis.org

242590, 1175444, 2416288, 2583146, 2596049, 2796151, 4953911, 5574794, 6127655, 6396209, 6460877, 6625438, 8521234, 11025856, 11352491, 15482298, 16228703, 18861024, 19048003, 20043534, 22835193, 31519781, 34399756

Offset: 1

Frank Ellermann, Dec 03 2001

nonn

			a(1)=242590 because 210*a(1) - 105 = 50943795 and 50943795 -2, - 4, - 8, - 16, + 2, + 4, + 8 and + 16 are all prime.

Harry J. Smith, Table of n, a(n) for n = 1..100

A proper subset of A061671 (prime sextets). Cf. prime quadruples A014561. See also A066081.

With[{c=2^Range[4]},Select[Range[35*10^6],AllTrue[Flatten[210#-105+ {c,-c}], PrimeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 10 2015 *)

{ n=0; for (m=1, 10^12, b=210*m - 105; c=0; for (j=1, 4, if (isprime(b - 2^j) , c++, break)); if (c<4, next); for (j=1, 4, if (isprime(b + 2^j) , c++, break)); if (c == 8, write("b066082.txt", n++, " ", m); if (n==100, return)) ) } \\ Harry J. Smith, Nov 11 2009

More terms from Don Reble, Dec 07 2001

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A083409 Number of prime k-tuplet constellations, i.e., patterns with minimal diameter A008407.

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A066081 a(n) = smallest m such that m+2^j and m-2^j are prime for all 0 < j <= n.

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A066082 Prime octets: numbers k such that 210*k - 105 +- 2^j are prime for all 1 <= j <= 4.

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