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A229348 Numerators of the ordinary convergents of continued fraction [x(1),x(2),x(3),...], where x(n) = F(n+1)/F(n), F = A000045 (Fibonacci numbers). 6
1, 3, 4, 7, 193, 200, 3393, 2273510, 20464983, 63668459, 147801901, 211470360, 2896916581, 3108386941, 15330464345, 18438851286, 33769315631, 52208166917, 347018317133, 399226484050, 4738509641683, 9876245767416, 14614755409099, 39105756585614 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Suppose that x(n) is a sequence of positive real numbers with divergent sum. By the Seidel Convergence Theorem, the continued fraction [x(1),x(2),x(3),...] converges.
LINKS
EXAMPLE
[1, 2/1, 3/2, 5/3, 8/5,...] = 1.3985985... The first 5 ordinary convergents are 1, 3/2, 4/3, 7/5, 193/138.
MATHEMATICA
z = 500; t = Table[Fibonacci[n + 1]/Fibonacci[n], {n, z}]
r = FromContinuedFraction[t]; c = Convergents[r, z];
Numerator[c] (* A229348 *)
Denominator[c] (* A229349 *)
RealDigits[r, 10, 120] (* A229350 *)
CROSSREFS
Sequence in context: A100978 A059077 A042707 * A215758 A011215 A093592
KEYWORD
nonn,frac,easy
AUTHOR
Clark Kimberling, Sep 21 2013
STATUS
approved

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Last modified April 20 06:53 EDT 2024. Contains 371799 sequences. (Running on oeis4.)