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A222424
Numbers n such that n and n + 14 are prime and there is a power of two in the interval (n,n+14).
1
3, 5, 23, 29, 53, 59, 509, 1019, 2039, 262133, 262139, 536870909, 73786976294838206459, 2787593149816327892691964784081045188247543
OFFSET
1,1
COMMENTS
It is a conjecture that this is a finite sequence. A search was conducted out to 2^1500.
PROG
(Magma)
//Program finds primes separated by an even number (called gap) which
//have a power of two between them. Program starts with the smallest
//power of two above gap. Primes less than this starting point can be
//checked by inspection.
gap:=14;
start:=Ilog2(gap)+1;
for i:= start to 1000 do
powerof2:=2^i;
for k:=powerof2-gap+1 to powerof2-1 by 2 do
if (IsPrime(k) and IsPrime(k+gap)) then k;
end if;
end for;
end for;
CROSSREFS
Sequence in context: A270912 A137084 A271347 * A067256 A136891 A296920
KEYWORD
nonn
AUTHOR
Brad Clardy, Feb 24 2013
STATUS
approved