Search: id:A006338
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%I A006338 M0087
%S A006338 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,
%T A006338 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,
%U A006338 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
%N A006338 An "eta-sequence": [ (n+1)*sqrt(2) + (1/2) ] - [ n*sqrt(2) + (1/2) ].
%C A006338 Equals its own "second derivative" (cf. A006337).
%C A006338 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.
%D A006338 Douglas Hofstadter, "Fluid Concepts and Creative Analogies", Chapter 
               1: "To seek whence cometh a sequence".
%D A006338 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%Y A006338 Cf. A006337.
%Y A006338 Sequence in context: A022300 A105690 A006337 this_sequence A020903 A133083 
               A083921
%Y A006338 Adjacent sequences: A006335 A006336 A006337 this_sequence A006339 A006340 
               A006341
%K A006338 nonn,easy,nice
%O A006338 1,1
%A A006338 D. R. Hofstadter
%E A006338 More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 
               28 2003

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