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%I #18 Sep 08 2022 08:46:04
%S 3,7,13,31,241,65521,1048573,2305843009213693951
%N Numbers n such that n and n + 16 are prime and there is a power of two in the interval (n,n+16).
%C It is a conjecture that this is a finite sequence. A search was conducted out to 2^1500.
%o (Magma)
%o //Program finds primes separated by an even number (called gap) which
%o //have a power of two between them. Program starts with the smallest
%o //power of two above gap. Primes less than this starting point can be
%o //checked by inspection.
%o gap:=16;
%o start:=Ilog2(gap)+1;
%o for i:= start to 1000 do
%o powerof2:=2^i;
%o for k:=powerof2-gap+1 to powerof2-1 by 2 do
%o if (IsPrime(k) and IsPrime(k+gap)) then k;
%o end if;
%o end for;
%o end for;
%Y Cf. A049488, A221211.
%K nonn
%O 1,1
%A _Brad Clardy_, Feb 23 2013
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