id:A092053 - OEIS Search Results

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A092053

Denominators of the convergents of the continued fraction expansion [1;1/2,1/3,1/4,...,1/n,...].

+0
2

1, 1, 7, 19, 53, 81, 823, 5359, 12923, 21877, 102061, 354883, 808865, 1433689, 25699639, 369784999, 817787423, 1487830821, 6512750579, 23917578595, 51908057021, 96040578001, 827937066989, 6166467806391, 13211837015707 (list; graph; listen)

	OFFSET	`1,3`
	COMMENT	`Numerators of convergents are A001902 (successive denominators of Wallis's product approximation to Pi/2). Sum of numerators and denominators equals powers of 2: A001902(n) + a(n) = 2^A092054(n).`
	FORMULA	`a(n) = 2^A092054(n) - A001902(n).`
	PROGRAM	`(PARI) a(n)=local(A); CF=contfracpnqn(vector(n, k, 1/k)); A=denominator(CF[1, 1]/CF[2, 1])`
	CROSSREFS	`Cf. A001902, A092054.` `Sequence in context: A027523 A100545 A100450 this_sequence A072630 A002714 A126361` `Adjacent sequences: A092050 A092051 A092052 this_sequence A092054 A092055 A092056`
	KEYWORD	`frac,nonn`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), Feb 19 2004`

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Last modified July 26 23:19 EDT 2008. Contains 142293 sequences.

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