id:A133570 - OEIS Search Results

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"Exact" continued fraction of e.

+0
1

3, -4, 2, 5, -2, -7, 2, 9, -2, -11, 2, 13, -2, -15, 2, 17, -2, -19, 2, 21, -2, -23, 2, 25, -2, -27, 2, 29, -2, -31, 2, 33, -2, -35, 2, 37, -2, -39, 2, 41, -2, -43, 2, 45, -2, -47, 2, 49, -2, -51, 2, 53, -2, -55, 2, 57, -2, -59, 2, 61, -2, -63, 2, 65, -2, -67, 2, 69, -2, -71, 2, 73, -2, -75, 2, 77, -2, -79, 2, 81, -2, -83, 2, 85, -2, -87, 2 (list; graph; listen)

	OFFSET	`0,1`
	COMMENT	`See comments in A133593. Just as for the usual continued fraction for e, the exact continued fraction also has a simple pattern.`
	FORMULA	`x(0)=e, a(n) = floor( \|x(n)\| + 0.5 ) * Sign(x(n)), x(n+1) = 1 / (x(n)-a(n)).`
	CROSSREFS	`Cf. A133593 A003417.` `Sequence in context: A078069 A090131 A139525 this_sequence A117041 A143939 A138609` `Adjacent sequences: A133567 A133568 A133569 this_sequence A133571 A133572 A133573`
	KEYWORD	`cofr,sign`
	AUTHOR	`Serhat Sevki Dincer (jfcgauss(AT)gmail.com), Dec 30 2007`

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Last modified December 4 20:00 EST 2008. Contains 151309 sequences.

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