A219013 Denominators in a product expansion for sqrt(3).

11, 523451, 39571031999225940638473470251

Offset

0,1

Comments

The product expansion in question is sqrt(3) = product {n = 0..inf} (1 + 2*A219012(n)/A219013(n)) = (1 + 2*4/11)*(1 + 2*724/523451)*(1 + 2*198924689265124/39571031999225940638473470251)*....

Links

Table of n, a(n) for n=0..2.

Formula

Let alpha = 1/2*(sqrt(2) + sqrt(6)) and put f(n) = 1/sqrt(6)*{alpha^n - (-1/alpha)^n}. Then a(n) = f(5^(n+1))/f(5^n).

a(n) = A219012(n)^2 - A219012(n) - 1.

Recurrence equation: a(n+1) = 5/2*(a(n)^4 - a(n)^2)*sqrt(4*a(n) + 5) + a(n)^5 + 15/2*a(n)^4 - 25/2*a(n)^2 + 5 with initial condition a(0) = 11.

Crossrefs

Cf. A219011, A219012, A219015.

Sequence in context: A297057 A090102 A320625 * A243130 A253632 A112854

Adjacent sequences: A219010 A219011 A219012 * A219014 A219015 A219016

Keyword

nonn,easy,bref

Author

Peter Bala, Nov 09 2012

Status

approved