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A332535 Numbers that are not of the form p + 2^(2^k) + 2^q with p, q primes and k >= 0.

%I A332535 #17 Nov 27 2020 07:04:42
%S A332535 1,2,3,4,5,6,7,16,18,20,24,28,30,32,34,40,42,44,46,48,52,54,56,58,60,
%T A332535 62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,
%U A332535 106,108,110,112,114,116,118,120,122,124,126,128,130,136,138
%N A332535 Numbers that are not of the form p + 2^(2^k) + 2^q with p, q primes and k >= 0.
%H A332535 Alois P. Heinz, <a href="/A332535/b332535.txt">Table of n, a(n) for n = 1..10000</a>
%H A332535 Christian Elsholtz, Florian Luca, and Stefan Planitzer, <a href="https://doi.org/10.1007/s11139-017-9972-8">Romanov type problems</a>, The Ramanujan Journal 47.2 (2018): 267-289.
%p A332535 q:= proc(n) local k, i;
%p A332535       for k from 0 while 2^(2^k)<n do
%p A332535         for i while 2^(2^k)+2^ithprime(i)<n do
%p A332535           if isprime(n-2^(2^k)-2^ithprime(i)) then return false fi:
%p A332535         od
%p A332535       od; true
%p A332535     end:
%p A332535 select(q, [$1..200])[];  # _Alois P. Heinz_, Feb 15 2020
%t A332535 q[n_] := Module[{k, i}, For[k = 0 , 2^(2^k) < n, k++, For[i = 1, 2^(2^k) + 2^Prime[i] < n, i++, If[PrimeQ[n - 2^(2^k) - 2^Prime[i]], Return[False]]] ]; True];
%t A332535 Select[Range[200], q] (* _Jean-François Alcover_, Nov 27 2020, after _Alois P. Heinz_ *)
%Y A332535 Cf. A218044, A332379, A332534.
%K A332535 nonn
%O A332535 1,2
%A A332535 _N. J. A. Sloane_, Feb 15 2020