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 A118242 #14 Feb 16 2025 08:33:01
%S A118242 1,2,4,17,19,5777,5779,192900153617,192900153619,
%T A118242 7177905237579946589743592924684177,7177905237579946589743592924684179
%N A118242 Pierce expansion of 1/phi.
%C A118242 Differs from A006276 in the first term only.
%H A118242 G. C. Greubel, <a href="/A118242/b118242.txt">Table of n, a(n) for n = 1..17</a>
%H A118242 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PierceExpansion.html">Pierce Expansion</a>
%F A118242 A118242(n) = A006276(n-1) for n>1.
%F A118242 From _Peter Bala_, Dec 03 2012: (Start)
%F A118242 Odd-indexed terms give A002813; even-indexed terms give A002814.
%F A118242 The Pierce series expansion is the alternating series 1/phi = 1/2*(sqrt(5) - 1) = 1/1 - 1/(1*2) + 1/(1*2*4) - 1/(1*2*4*17) + 1/(1*2*4*17*19) - ....
%F A118242 Another series expansion is
%F A118242 1/phi = a(1)/a(2) + (a(1)*a(3))/(a(2)*a(4)) + (a(1)*a(3)*a(5))/(a(2)*a(4)*a(6)) + ... = 1/2 + (1*4)/(2*17) + (1*4*19)/(2*17*5777) + ....
%F A118242 (End)
%t A118242 PierceExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@ NestList[{Floor[1/Expand[1 - #[[1]] #[[2]]]], Expand[1 - #[[1]] #[[2]]]} &, {Floor[1/(A - Floor[A])], A - Floor[A]}, n - 1]]; PierceExp[N[(Sqrt[5] - 1)/2, 7!], 10] (* _G. C. Greubel_, Nov 14 2016 *)
%Y A118242 Cf. A006276. A002813, A002814.
%K A118242 nonn,easy
%O A118242 1,2
%A A118242 _Eric W. Weisstein_, Apr 17 2006