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 A220951 Primes p such that p+6 is also prime and there is a power of two in the interval (p,p+6). 2
 5, 7, 11, 13, 31, 61, 251, 4093 (list; graph; refs; listen; history; text; internal format)
 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^n-k, plus a few additional tests, we have a(9) > 2^750740. - Giovanni Resta, Feb 21 2013 LINKS 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:=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 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

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Last modified December 1 21:20 EST 2021. Contains 349435 sequences. (Running on oeis4.)