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%I #13 Nov 15 2016 02:42:37
%S 1,2,4,17,19,5777,5779,192900153617,192900153619,
%T 7177905237579946589743592924684177,7177905237579946589743592924684179
%N Pierce expansion of 1/phi.
%C Differs from A006276 in the first term only.
%H G. C. Greubel, <a href="/A118242/b118242.txt">Table of n, a(n) for n = 1..17</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PierceExpansion.html">Pierce Expansion</a>
%F A118242(n) = A006276(n-1) for n>1.
%F From _Peter Bala_, Dec 03 2012: (Start)
%F Odd-indexed terms give A002813; even-indexed terms give A002814.
%F 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 Another series expansion is
%F 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 (End)
%t 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 Cf. A006276. A002813, A002814.
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_, Apr 17 2006
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