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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Dec 13 2019
STATUS
approved