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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 28 13:47 EST 2021. Contains 349413 sequences. (Running on oeis4.)