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A245516 The smallest odd number k such that k^n-2 is a prime number.

%I A245516 #12 Jul 08 2016 09:48:38
%S A245516 5,3,9,3,3,3,7,7,3,21,9,7,19,5,7,39,15,61,15,19,21,3,19,17,21,5,21,7,
%T A245516 85,17,7,21,511,27,27,59,3,19,91,45,3,29,321,65,9,379,69,125,49,5,9,
%U A245516 45,289,341,61,89,171,171,139,21,139,75,25,49,15,51,57,175
%N A245516 The smallest odd number k such that k^n-2 is a prime number.
%H A245516 Zak Seidov, <a href="/A245516/b245516.txt">Table of n, a(n) for n = 1..200</a>
%e A245516 n=1, 3-2=1 is not prime, 5-2=3 is a prime number.  So a(1) = 5.
%e A245516 n=2, 3^2-2=7 is a prime number.  So a(2) = 3.
%e A245516 n=10, for k=3, 5, ..., 19, k^10-2 are all composite.  21^10-2 = 16679880978199 is a prime number.  So a(10) = 21.
%p A245516 A245516 := proc(n)
%p A245516     for k from 1 by 2 do
%p A245516         if isprime(k^n-2) then
%p A245516             return k;
%p A245516         end if;
%p A245516     end do:
%p A245516 end proc:
%p A245516 seq(A245516(n),n=1..60) ;
%t A245516 Table[n = 1;
%t A245516 While[n = n + 2; cp = n^i - 2; ! PrimeQ[cp]]; n, {i, 1, 68}]
%Y A245516 Cf. A095303.
%K A245516 nonn
%O A245516 1,1
%A A245516 _Lei Zhou_, Jul 24 2014