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%I #35 Nov 23 2019 04:08:51
%S 1,0,1,0,1,2,1,0,1,2,3,2,3,2,1,0,1,2,3,4,3,4,5,4,5,4,3,4,3,2,1,0,1,2,
%T 3,4,5,4,5,6,7,6,7,8,7,8,7,6,7,8,7,8,7,6,7,6,5,4,5,4,3,2,1,0,1,2,3,4,
%U 5,6,5,6,7,8,9,8,9,10,11,10,11,12,11,12,11,10,11,12,13,12,13,14,13,14,13,12
%N a(n) = 2*A004001(n) - n, where A004001 is the Hofstadter-Conway $10000 sequence.
%C The sequence is 0 at 2^n for n = 1, 2, 3, ... The maximum value between 2^n and 2^(n+1) appears to be A072100(n). - _T. D. Noe_, Jun 04 2012
%C Hofstadter shows the plot of sequence A004001(n)-(n/2) at point 10:52 of the part two of DIMACS lecture. This sequence is obtained by doubling those values, thus producing only integers. Cf. also A249071. - _Antti Karttunen_, Oct 22 2014
%H T. D. Noe (first 10000 terms) and Antti Karttunen, <a href="/A004074/b004074.txt">Table of n, a(n) for n = 1..16384</a>
%H D. R. Hofstadter, Analogies and Sequences: Intertwined Patterns of Integers and Patterns of Thought Processes, Lecture in DIMACS Conference on Challenges of Identifying Integer Sequences, Rutgers University, October 10 2014; <a href="http://vimeo.com/109139374">Part 1</a>, <a href="http://vimeo.com/109139377">Part 2</a>.
%H T. Kubo and R. Vakil, <a href="http://dx.doi.org/10.1016/0012-365X(94)00303-Z">On Conway's recursive sequence</a>, Discr. Math. 152 (1996), 225-252.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Blancmange_curve">Blancmange curve</a>
%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%F a(2^n)=0; for n >= 1, Sum_{i=2^(n-1)..2^n} a(i) = A082590(n-2). - _Benoit Cloitre_, Jun 04 2004
%t Clear[a]; a[1] = 1; a[2] = 1; a[n_] := a[n] = a[a[n - 1]] + a[n - a[n - 1]]; Table[2*a[n] - n, {n, 100}] (* _T. D. Noe_, Jun 04 2012 *)
%o (Scheme) (define (A004074 n) (- (* 2 (A004001 n)) n)) ;; Other code as in A004001. - _Antti Karttunen_, Oct 22 2014
%Y Cf. A004001, A082590, A213057.
%Y Cf. also A249071 (gives the even bisection halved), A233270 (also has a similar Blancmange curve appearance).
%K nonn
%O 1,6
%A _N. J. A. Sloane_
%E More terms from _Benoit Cloitre_, Jun 04 2004
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