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Smallest k such that both prime(k)*prime(k+1) +/- 2^n are prime, or 0 if no such k exists.
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%I #12 Jun 27 2014 16:09:47

%S 1,2,2,2,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Smallest k such that both prime(k)*prime(k+1) +/- 2^n are prime, or 0 if no such k exists.

%C a(n) = 0 for n > 5?

%C a(n) = 0 for 5 < n <= 10000. Heuristics suggest that there are no other nonzero terms. - _Charles R Greathouse IV_, Jun 04 2014

%e a(0) = 1 because prime(1)*prime(1+1)-2^0 = 5 and prime(1)*prime(1+1) + 2^0 = 7 are prime,

%e a(1) = 2 because prime(2)*prime(2+1)-2^1 = 13 and prime(2)*prime(2+1)+2^1 = 17 are prime,

%e a(2) = 2 because prime(2)*prime(2+1)-2^2 = 11 and prime(2)*prime(2+1)+2^2 = 19 are prime,

%e a(3) = 2 because prime(2)*prime(2+1)-2^3 = 7 and prime(2)*prime(2+1)+2^3 = 23 are prime.

%Y Cf. A006094.

%K nonn,less

%O 0,2

%A _Juri-Stepan Gerasimov_, Jun 03 2014