A193746 Smallest k such that k*n^2 +1 is an n-th power.

1, 2, 7, 5, 311, 434, 42799, 90075, 12345679, 34867844, 6140565047, 1695421, 4696537119847, 20088655029078, 5124095576030431, 25657845139503479, 7563707819165039903, 43404581642184336392, 14523213296398891966759

Offset: 1

Author

Michel Lagneau, Aug 03 2011

Keywords

• nonn

Examples

			a(9) = 12345679 because 12345679*9^2+1 = 1000000000 = 10^9.
		

Crossrefs

Cf. A076943.

Programs

Mathematica

a={}; Do[k = 2;While[ !IntegerQ[(k^n - 1)/n^2], k++ ]; AppendTo[a,(k^n-1)/n^2], {n, 1, 20}]; a

PARI

a(n)=my(k);while(!ispower(k++*n^2+1,n),);k \\ Charles R Greathouse IV, May 15 2013