

A220951


Primes p such that p+6 is also prime and there is a power of two in the interval (p,p+6).


2




OFFSET

1,1


COMMENTS

A search for sexy primes bracketing a power of two was conducted up to 2^1500. It is conjectured that this is a finite sequence.
On the basis of existing work about primes of the form 2^n+k and 2^nk, plus a few additional tests, we have a(9) > 2^750740.  Giovanni Resta, Feb 21 2013


LINKS

Table of n, a(n) for n=1..8.


MATHEMATICA

pptQ[n_]:=AllTrue[{n, n+6}, PrimeQ]&&Count[Log[2, #]&/@Range[n, n+6], _?IntegerQ] > 0; Select[Range[4100], pptQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 01 2015 *)


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:=6;
start:=Ilog2(gap)+1;
for i:= start to 1000 do
powerof2:=2^i;
for k:=powerof2gap+1 to powerof21 by 2 do
if (IsPrime(k) and IsPrime(k+gap)) then
k;
end if;
end for;
end for;


CROSSREFS

Cf. A023201, A220746, A221211.
Sequence in context: A135930 A163429 A339953 * A136055 A250127 A181494
Adjacent sequences: A220948 A220949 A220950 * A220952 A220953 A220954


KEYWORD

nonn,more


AUTHOR

Brad Clardy, Feb 20 2013


STATUS

approved



