A218490 - OEIS

%I #32 Jan 23 2022 07:35:19

%S 1,3,5,7,8,7,8,4,0,7,6,1,2,1,0,5,7,0,1,3,8,7,4,3,9,7,0,9,7,6,0,6,0,7,

%T 1,8,5,5,7,8,6,0,5,8,6,5,2,9,5,6,7,8,7,0,4,4,9,6,8,7,8,2,5,4,3,8,4,0,

%U 7,1,9,1,1,0,3,4,8,6,2,3,3,6,8,7,7,1,4

%N Decimal expansion of Lucas factorial constant.

%C The Lucas factorial constant is associated with the Lucas factorial A135407.

%H G. C. Greubel, <a href="/A218490/b218490.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals exp( Sum_{k>=1} 1/(k*(((3-sqrt(5))/2)^k-(-1)^k)) ). - _Vaclav Kotesovec_, Jun 08 2013

%F Equals Product_{k=0..infinity} (1 + (-1)^k/phi^(2*k)). - _G. C. Greubel_, Dec 23 2017

%F Equals lim_{n->oo} A135407(n)/phi^(n*(n+1)/2), where phi is the golden ratio (A001622). - _Amiram Eldar_, Jan 23 2022

%e 1.35787840761210570138743970976060718557860586529567870449687825438407191103...

%t RealDigits[QPochhammer[-1, -1/GoldenRatio^2], 10, 105][[1]] (* slightly modified by _Robert G. Wilson v_, Dec 21 2017 *)

%o (PARI) prodinf(j=0, 1 + ((sqrt(5) - 3)/2)^j) \\ _Iain Fox_, Dec 21 2017

%Y Cf. A062073, A135407, A070825, A003266, A000032, A000045, A186269, A001622.

%K nonn,cons

%O 1,2

%A _Vaclav Kotesovec_, Oct 30 2012