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 A105941 #17 Feb 16 2025 08:32:57
%S A105941 1,2,3,4,7,8,9,11,16,18,27,29,32,47,49,64,76,81,121,123,128,199,243,
%T A105941 256,322,324,343,512,521,729,841,843,1024,1331,1364,2048,2187,2207,
%U A105941 2209,2401,3571,4096,5776,5778,5832,6561,8192,9349,14641,15127,15129,16384
%N A105941 Powers of Lucas numbers.
%D A105941 A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 56.
%D A105941 Thomas Koshy, "Fibonacci and Lucas Numbers and Applications", Wiley, New York, 2001.
%D A105941 V. E. Hoggatt, Jr., Fibonacci and Lucas Numbers. Houghton, Boston, MA, 1969.
%H A105941 T. D. Noe, <a href="/A105941/b105941.txt">Table of n, a(n) for n = 1..1000</a>
%H A105941 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LucasNumber.html">Lucas Number.</a>
%F A105941 {a(n)} = {A000204} U {A001254} U {A075155} U {A099923} U {A103325}... L(n)^2 = L(2n) + 2(-1)^n = L(n-1)*L(n+1) + 5(-1)^n. L(n)^3 = L(3n) + 3(-1)^n*L(n). L(n)^4 = L(4n) + 4(-1)^n*L(2n) + 6. L(n)^5 = L(5n) + 5(-1)^n*L(3n) + 10L(n).
%t A105941 lim = 10^5; t = Table[f = LucasL[n]; If[f == 1, {1}, f^Range[Floor[Log[lim]/Log[f]]]], {n, 0, Floor[Log[GoldenRatio, lim]]}]; Union[Flatten[t]] (* _T. D. Noe_, Sep 27 2011 *)
%Y A105941 A000032 Lucas numbers. A001254 Squares of Lucas numbers. A075155 Cubes of Lucas numbers. A099923 Fourth powers of Lucas numbers. A103325 Fifth powers of Lucas numbers. A103324 Square array T(n, k) read by antidiagonals: powers of Lucas numbers. A105317 Powers of Fibonacci numbers.
%Y A105941 Cf. A000032, A001254, A075155, A099923, A103325, A103324, A105317.
%K A105941 easy,nonn
%O A105941 1,2
%A A105941 _Jonathan Vos Post_, Apr 27 2005
%E A105941 Corrected by _T. D. Noe_, Sep 26 2011