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Least k such that one of 2^n +- 2^k +- 1 is prime, where 0 < k < n, or 0 if there is no such prime.
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%I #13 Oct 30 2023 07:25:12

%S 1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,3,1,3,1,12,2,11,1,1,1,1,2,3,9,

%T 5,2,3,3,3,4,5,4,8,3,7,4,2,6,17,14,6,12,2,5,1,2,3,6,11,5,1,16,8,8,20,

%U 2,1,5,7,19,6,4,19,8,5,4,5,3,9,6,4,3,13,1,24

%N Least k such that one of 2^n +- 2^k +- 1 is prime, where 0 < k < n, or 0 if there is no such prime.

%C Does a(n) = 0 for some n?

%H Giovanni Resta, <a href="/A238900/b238900.txt">Table of n, a(n) for n = 2..10000</a> (first 1999 terms from T. D. Noe)

%t Table[c1 = 2^n; k = 1; While[c2 = 2^k; k < n && ! (PrimeQ[c1 + c2 + 1] || PrimeQ[c1 + c2 - 1] || PrimeQ[c1 - c2 + 1] || PrimeQ[c1 - c2 - 1]), k++]; If[k == n, 0, k], {n, 2, 100}]

%Y Cf. A196697.

%K nonn

%O 2,10

%A _T. D. Noe_, Mar 17 2014