cp's OEIS Frontend

A221211 Numbers n such that n and n + 4 are prime and there is a power of two in the interval (n,n+4).

%I A221211 #23 Sep 08 2022 08:46:04
%S A221211 3,7,13,127
%N A221211 Numbers n such that n and n + 4 are prime and there is a power of two in the interval (n,n+4).
%C A221211 It is a conjecture that this is a finite sequence. These may be the only known cousin primes with this property.
%C A221211 The Cf.s list similar sequences, of the form -- numbers n such that n and n+m are prime and contain a power of two in the interval (n,n+m). The case where m=2, the twin prime case -- not listed, has only one member n=3. Another member would have to be a twin where n+2 was a Fermat type prime and n a Mersenne prime.
%o A221211 (Magma)
%o A221211 //Program finds primes separated by an even number (called gap) which
%o A221211 //have a power of two between them. The program starts with the smallest
%o A221211 //of two above gap. Primes less than this starting point can be checked by
%o A221211 //inspection. In this example 3 also works.
%o A221211 gap:=4;
%o A221211 start:=Ilog2(gap)+1;
%o A221211 for i:= start to 1000 do
%o A221211     powerof2:=2^i;
%o A221211     for k:=powerof2-gap+1 to powerof2-1 by 2 do
%o A221211         if (IsPrime(k) and IsPrime(k+gap)) then k;
%o A221211         end if;
%o A221211     end for;
%o A221211 end for;
%o A221211 (Magma) [n: n in PrimesUpTo(10^3) | IsPrime(n+4) and exists{t: t in [n+1..n+3 by 2] | IsOne(t/2^Valuation(t,2))}]; // _Bruno Berselli_, May 16 2013
%Y A221211 Cf. A023200.
%Y A221211 Cf. A220951 (gap of 6), A213210 (8), A220746 (10), A213677 (12), A222424 (14), A222227 (16), A222219 (18).
%K A221211 nonn
%O A221211 1,1
%A A221211 _Brad Clardy_, Feb 21 2013