A330284 Numbers k such that both k and k+2 are de Polignac numbers (A006285).

905, 3341, 3431, 4151, 4811, 4841, 5729, 7387, 7811, 8921, 10235, 10511, 11081, 11435, 12371, 12731, 13091, 14021, 14141, 14381, 14531, 15041, 15119, 16025, 16865, 17369, 18209, 18611, 18895, 18897, 20141, 20321, 20381, 20651, 21671, 24131, 24431, 24461, 24731

Offset: 1

Author

Amiram Eldar, Dec 13 2019

Keywords

• nonn

Comments

The first 3 pairs are given in the book by Wells.

Examples

			905 is in the sequence since both 905 and 905 + 2 = 907 are de Polignac numbers.
		

References

• Alfred S. Posamentier and Ingmar Lehmann, Mathematical Curiosities: A Treasure Trove of Unexpected Entertainments, Prometheus Books, 2014, Chapter 1.
• David Wells, Prime Numbers: The Most Mysterious Figures in Math, John Wiley & Sons Inc., Hoboken, New Jersey, 2005, page 176.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Clifford A. Pickover, The Grand Internet Obstinate Number Search.
• Carlos Rivera, Puzzle 219. Polignac numbers, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A006285.

Programs

Mathematica

dePolQ[n_] := AllTrue[n - 2^Range[Floor[Log[2, n]]], !PrimeQ[#] &]; seq = {}; q1 = False; Do[q2 = dePolQ[n]; If[q1 && q2, AppendTo[seq, n - 2]]; q1 = q2, {n, 3, 25000, 2}]; seq