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A330284
Numbers k such that both k and k+2 are de Polignac numbers (A006285).
2
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Dec 13 2019
STATUS
approved