id:A135455 - OEIS Search Results

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Numbers n such that n*phi is within 0.1 of an integer, where phi is the golden ratio.

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5, 8, 13, 21, 26, 29, 34, 42, 47, 50, 55, 60, 63, 68, 76, 81, 84, 89, 94, 97, 102, 110, 115, 118, 123, 131, 136, 139, 144, 149, 152, 157, 165, 170, 173, 178, 186, 191, 199, 204, 207, 212, 220, 225, 228, 233, 238, 241, 246, 254, 259, 262, 267, 275, 280, 283, 288 (list; graph; listen)

	OFFSET	`1,1`
	COMMENT	`By using the formula of Binet one can easily show that all Fibonacci numbers greater than 3 are in the sequence. Furthermore the sequence a(n)/n converges to 1/5.`
	EXAMPLE	`47 is in the sequence because 1.6180339887*47 = 76.047 which is within .1 of an integer.`
	MATHEMATICA	`Select[Range[300], Abs[ #(1 + Sqrt[5])/2 - Round[ #(1 + Sqrt[5])/2]] < 0.1 &]`
	CROSSREFS	`Cf. A000045.` `Sequence in context: A097404 A020687 A035423 this_sequence A020712 A111321 A020736` `Adjacent sequences: A135452 A135453 A135454 this_sequence A135456 A135457 A135458`
	KEYWORD	`easy,nonn`
	AUTHOR	`Ben Thurston (benthurston27(AT)yahoo.com), Dec 15 2007`
	EXTENSIONS	`Edited and extended by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Feb 20 2008`

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.

AT&T Labs Research