A088039 Smallest k such that k^3 == 1 (mod some n-th power), k > 1.

2, 4, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145, 524289, 1048577, 2097153, 4194305, 8388609, 16777217, 33554433, 67108865, 134217729, 268435457, 536870913, 1073741825, 2147483649

Offset: 1

Author

Amarnath Murthy, Sep 19 2003

Keywords

• nonn

Comments

In most of the cases the n-th power that divides a(n)^3-1 is 2^n.

Crossrefs

Cf. A088038.

Cf. A020737. [From R. J. Mathar, Sep 11 2008]

Formula

a(n) = A088038(n)^(1/3).

Conjecture: a(n) = 2^n+1 for n>2. a(n) = 3*a(n-1)-2*a(n-2) for n>4. G.f.: -x*(2*x^3-x^2+2*x-2) / ((x-1)*(2*x-1)). [Colin Barker, Feb 05 2013]

Extensions

Corrected and extended by Ray Chandler, Oct 04 2003