|
%I #29 Dec 14 2019 08:09:48
%S 905,3341,3431,4151,4811,4841,5729,7387,7811,8921,10235,10511,11081,
%T 11435,12371,12731,13091,14021,14141,14381,14531,15041,15119,16025,
%U 16865,17369,18209,18611,18895,18897,20141,20321,20381,20651,21671,24131,24431,24461,24731
%N Numbers k such that both k and k+2 are de Polignac numbers (A006285).
%C The first 3 pairs are given in the book by Wells.
%D Alfred S. Posamentier and Ingmar Lehmann, Mathematical Curiosities: A Treasure Trove of Unexpected Entertainments, Prometheus Books, 2014, Chapter 1.
%D David Wells, Prime Numbers: The Most Mysterious Figures in Math, John Wiley & Sons Inc., Hoboken, New Jersey, 2005, page 176.
%H Amiram Eldar, <a href="/A330284/b330284.txt">Table of n, a(n) for n = 1..10000</a>
%H Clifford A. Pickover, <a href="http://sprott.physics.wisc.edu/pickover/obstinate.html">The Grand Internet Obstinate Number Search</a>.
%H Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_219.htm">Puzzle 219. Polignac numbers</a>, The Prime Puzzles & Problems Connection.
%e 905 is in the sequence since both 905 and 905 + 2 = 907 are de Polignac numbers.
%t 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
%Y Cf. A006285.
%K nonn
%O 1,1
%A _Amiram Eldar_, Dec 13 2019
|
