cp's OEIS Frontend

A213210 Numbers n such that n and n + 8 are prime and there is a power of two in the interval (n,n+8).

%I A213210 #13 Sep 08 2022 08:46:02
%S A213210 3,5,11,29,59,4091,262139
%N A213210 Numbers n such that n and n + 8 are prime and there is a power of two in the interval (n,n+8).
%C A213210 It is a conjecture that this sequence is finite. A search around 2^n was done up to 2^1500.
%o A213210 (Magma)
%o A213210 //Program finds primes separated by an even number (called gap) which
%o A213210 //have a power of two between them. The program starts with the smallest
%o A213210 //power of two above gap. Primes less than this starting point can be
%o A213210 //checked inspection. In this example 3 and 5 also work.
%o A213210 gap:=8;
%o A213210 start:=Ilog2(gap)+1;
%o A213210 for i:= start to 1000 do
%o A213210     powerof2:=2^i;
%o A213210     for k:=powerof2-gap+1 to powerof2-1 by 2 do
%o A213210         if (IsPrime(k) and IsPrime(k+gap)) then k;
%o A213210         end if;
%o A213210     end for;
%o A213210 end for;
%o A213210 (Magma) [n: n in PrimesUpTo(10^6) | IsPrime(n+8) and exists{t: t in [n+1..n+7 by 2] | IsOne(t/2^Valuation(t,2))}]; // _Bruno Berselli_, May 16 2013
%Y A213210 Cf. A023202, A221211.
%K A213210 nonn
%O A213210 1,1
%A A213210 _Brad Clardy_, Mar 02 2013