The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #25 Feb 08 2024 04:54:31
%S 1117175145,2544265305,3147056235,3366991695,3472109835,3621922845,
%T 3861518805,4447794915,4848148485,5415281745,5693877405,7525056375,
%U 7602256605,9055691835,9217432215,13431856995,16819230075,19373391165,21468020835,24358769685,27002844795,30252463305,33359739795
%N De Polignac numbers k > 1 such that k - 2^m is a de Polignac number for every 1 < 2^m < k.
%C Odd integers k > 3 that are not of the form p + 2^m + 2^n with m,n >= 0, where p is a prime.
%C These are de Polignac numbers k > 1 in A156695. Numbers k in A156695 such that k - 2 is composite.
%C Problem: are there infinitely many such numbers?
%H Amiram Eldar, <a href="/A337487/b337487.txt">Table of n, a(n) for n = 1..204</a> (terms below 10^12, calculated using the b-file at A156695)
%t A156695 = Cases[Import["https://oeis.org/A156695/b156695.txt", "Table"], {_, _}][[;; , 2]]; dePolQ[n_] := n > 3 && AllTrue[n - 2^Range[Floor[Log[2, n]]], !PrimeQ[#] &]; Select[A156695, dePolQ] (* _Amiram Eldar_, Aug 29 2020 *)
%Y An intersection of A006285 > 1 and A156695 (with m,n >= 1).
%K nonn
%O 1,1
%A _Thomas Ordowski_, Aug 29 2020