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A219011 Denominators in a product expansion for sqrt(5). 4
5, 15005, 792070839820228500005 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Apart from the initial term same as A145275.

a(3) has 105 digits and a(4) has 523 digits.

The product expansion in question is sqrt(5) = product {n = 0..inf} (1 + 2*A219010(n)/A219011(n)) = (1 + 6/5)*(1 + 246/15005)*(1 + 56287506246/792070839820228500005)*....

LINKS

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

FORMULA

a(n) = Fibonacci(5^(n+1))/Fibonacci(5^n).

a(n) = A219010(n)^2 - A219010(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) = 5.

a(n) = Lucas(4*5^n) - Lucas(2*5^n) + 1. - Ehren Metcalfe, Jul 29 2017

PROG

(Maxima) A219011(n):=fib(5^(n+1))/fib(5^n)$

makelist(A219011(n), n, 0, 3);

CROSSREFS

Cf. A145275, A219010, A219013, A219015.

Sequence in context: A058051 A242772 A089989 * A297482 A185686 A083976

Adjacent sequences:  A219008 A219009 A219010 * A219012 A219013 A219014

KEYWORD

nonn,easy,bref

AUTHOR

Peter Bala, Nov 09 2012

STATUS

approved

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Last modified June 19 05:18 EDT 2021. Contains 345125 sequences. (Running on oeis4.)