This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A088039 #20 Mar 19 2021 09:54:21 %S A088039 2,4,9,17,33,65,129,257,513,1025,2049,4097,8193,16385,32769,65537, %T A088039 131073,262145,524289,1048577,2097153,4194305,8388609,16777217, %U A088039 33554433,67108865,134217729,268435457,536870913,1073741825,2147483649 %N A088039 Smallest k such that k^3 == 1 (mod some n-th power), k > 1. %C A088039 In most of the cases the n-th power that divides a(n)^3-1 is 2^n. %F A088039 a(n) = A088038(n)^(1/3). %F A088039 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] %Y A088039 Cf. A088038. %Y A088039 Cf. A020737. [From _R. J. Mathar_, Sep 11 2008] %K A088039 nonn %O A088039 1,1 %A A088039 _Amarnath Murthy_, Sep 19 2003 %E A088039 Corrected and extended by _Ray Chandler_, Oct 04 2003