id:A067992 - OEIS Search Results

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a(0)=1 and, for n>0, a(n) is the smallest positive integer such that the ratios min(a(k)/a(k-1),a(k-1)/a(k)) for 0<k<=n are all distinct.

+0
3

1, 1, 2, 3, 1, 4, 3, 5, 1, 6, 5, 2, 7, 1, 8, 3, 7, 4, 5, 7, 6, 11, 1, 9, 2, 11, 3, 10, 1, 12, 5, 8, 7, 9, 4, 11, 5, 9, 8, 11, 7, 10, 9, 11, 10, 13, 1, 14, 3, 13, 2, 15, 1, 16, 3, 17, 1, 18, 5, 13, 4, 15, 7, 12, 11, 13, 6, 17, 2, 19, 1, 20, 3, 19, 4, 17, 5, 14, 9, 13, 7, 16, 5, 19, 6, 23, 1, 21, 2 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`Every positive rational number appears exactly once as the ratio of adjacent terms (in either order). Conjecture: adjacent terms are always relatively prime. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 13 2006`
	FORMULA	`a(6)=3, since 1/4 and 2/4=1/2 have already occurred as ratios of adjacent terms.`
	CROSSREFS	`See A066720 for a somewhat similar sequence.` `Cf. A002487, A057979.` `Sequence in context: A125936 A161621 A095701 this_sequence A140757 A100035 A090244` `Adjacent sequences: A067989 A067990 A067991 this_sequence A067993 A067994 A067995`
	KEYWORD	`nonn,nice`
	AUTHOR	`John W. Layman (layman(AT)math.vt.edu), Feb 06 2002`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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