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

1,2

Links

Table of n, a(n) for n=1..19.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A076943.

Sequence in context: A094360 A335594 A051757 * A070524 A259830 A259235

Adjacent sequences: A193743 A193744 A193745 * A193747 A193748 A193749

Keyword

nonn

Author

Michel Lagneau, Aug 03 2011

Status

approved