id:A087950 - OEIS Search Results

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Numerators k for which the partial quotients of the k-CF of sqrt(2) are periodic, where a k-CF is defined as the continued fraction representation having k as the constant numerator: x = q_0 + k/(q_1 + k/(q_2 + k/(q_3 +...))).

+0
2

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 15, 17, 18, 20, 21, 25, 29, 30, 34, 35, 40, 41, 42, 45, 50, 51, 55, 58, 60, 63, 65, 68, 70, 84, 85, 87, 99, 102, 116, 119, 126, 136, 145, 153, 169, 170, 174, 187, 189, 198, 203, 204, 221, 232, 238, 239, 252, 255, 261, 272, 289, 290, 297 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`It is well-known that quadratic numbers have periodic partial quotients in simple continued fractions where the numerators are 1; it is unexpected that similar expressions of quadratics do not remain periodic for most constant numerators k>1.`
	CROSSREFS	`Cf. A087951.` `Sequence in context: A067175 A049809 A011870 this_sequence A060527 A079002 A119984` `Adjacent sequences: A087947 A087948 A087949 this_sequence A087951 A087952 A087953`
	KEYWORD	`nonn`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), Sep 16 2003`

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

AT&T Labs Research