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%I #11 May 13 2013 01:49:55
%S 1,2,91,5,1222981,13867245,4644275800711,3331605615,
%T 4806028313710522550281,1185520435892914104577275,
%U 1305063339568963727983307233802251,320735961523340363019772627010045
%N Smallest k such that k*2^n +1 is an n-th power.
%e a(3) = 91 because 91*2^3 + 1 = 729 = 9^3.
%t a={};Do[k = 2;While[ !IntegerQ[(k^n - 1)/2^n], k++ ]; AppendTo[a,(k^n-1)/2^n],{n, 1, 20}];a
%o (PARI) a(n)=if(n%2,(2^n+1)^n>>n,my(N=1<<n,m=3);while(Mod(m,N)^n!=1,m+=m+1);m^n>>n) \\ _Charles R Greathouse IV_, Aug 03 2011
%K nonn,easy
%O 1,2
%A _Michel Lagneau_, Aug 03 2011
%E a(9) corrected by _Charles R Greathouse IV_, Aug 03 2011