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

1,1

Comments

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

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.

Example

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

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

Crossrefs

Cf. A006285.

Sequence in context: A098237 A068856 A235949 * A330303 A181257 A235242

Adjacent sequences: A330281 A330282 A330283 * A330285 A330286 A330287

Keyword

nonn

Author

Amiram Eldar, Dec 13 2019

Status

approved