id:A006338 - OEIS Search Results

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An "eta-sequence": [ (n+1)*sqrt(2) + (1/2) ] - [ n*sqrt(2) + (1/2) ].
(Formerly M0087)

+0
3

2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2 (list; graph; listen)

	OFFSET	`1,1`
	COMMENT	`Equals its own "second derivative" (cf. A006337).` `Presumably this is the same as the following sequence from Hofstadter's book: the number of triangular numbers between each successive pair of squares. More precisely, a(n) is the number of triangular numbers T such that n^2 <= T < (n+1)^2. E.g. a(3) = 2 because 3^2 <= T < 4^2 permits T(4) = 10 and T(5) = 15, and no other triangular number. - Hugo van der Sanden (hv(AT)crypt.org), May 03 2005.`
	REFERENCES	`Douglas Hofstadter, "Fluid Concepts and Creative Analogies", Chapter 1: "To seek whence cometh a sequence".`
	CROSSREFS	`Cf. A006337.` `Sequence in context: A022300 A105690 A006337 this_sequence A020903 A133083 A083921` `Adjacent sequences: A006335 A006336 A006337 this_sequence A006339 A006340 A006341`
	KEYWORD	`nonn,easy,nice`
	AUTHOR	`D. R. Hofstadter`
	EXTENSIONS	`More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 28 2003`

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.

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