A193747 Smallest k such that k*2^n +1 is an n-th power.

1, 2, 91, 5, 1222981, 13867245, 4644275800711, 3331605615, 4806028313710522550281, 1185520435892914104577275, 1305063339568963727983307233802251, 320735961523340363019772627010045

Offset

1,2

Links

Table of n, a(n) for n=1..12.

Example

a(3) = 91 because 91*2^3 + 1 = 729 = 9^3.

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A306760 A306964 A138583 * A242176 A024240 A266653

Adjacent sequences: A193744 A193745 A193746 * A193748 A193749 A193750

Keyword

nonn,easy

Author

Michel Lagneau, Aug 03 2011

Extensions

a(9) corrected by Charles R Greathouse IV, Aug 03 2011

Status

approved