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A006338
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An "eta-sequence": [ (n+1)*sqrt(2) + (1/2) ] - [ n*sqrt(2) + (1/2) ].
(Formerly M0087)
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2
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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.
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REFERENCES
| Douglas Hofstadter, "Fluid Concepts and Creative Analogies", Chapter 1: "To seek whence cometh a sequence".
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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CROSSREFS
| Cf. A006337.
Sequence in context: A105690 A175922 A006337 * A020903 A133083 A083921
Adjacent sequences: A006335 A006336 A006337 * A006339 A006340 A006341
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KEYWORD
| nonn,easy,nice
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AUTHOR
| D. R. Hofstadter
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EXTENSIONS
| More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 28 2003
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