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A240808
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a(0)=2, a(1)=1, a(2)=0; thereafter a(n) = a(n-1-a(n-1))+a(n-2-a(n-2)) unless a(n-1) <= n-1 or a(n-2) <= n-2 in which case the sequence terminates.
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8
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2, 1, 0, 2, 1, 3, 2, 1, 3, 5, 4, 3, 5, 4, 6, 8, 4, 6, 8, 7, 9, 8, 7, 12, 11, 7, 12, 14, 10, 12, 14, 10, 12, 17, 13, 12, 20, 16, 12, 20, 19, 15, 20, 19, 18, 23, 19, 21, 26, 19, 21, 26, 19, 24, 29, 19, 27, 32, 19, 27, 32, 22, 30, 32, 22, 30, 32, 25, 33, 32, 28, 36, 32, 31, 39, 32, 31, 42, 35, 31, 45, 38, 31, 45, 38, 31, 48, 41, 31, 51, 44, 31, 51, 47, 34
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history;
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OFFSET
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0,1
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COMMENTS
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a(A241218(n)) = n and a(m) <> n for m < A241218(n). - Reinhard Zumkeller, Apr 17 2014
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REFERENCES
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Higham, Jeff and Tanny, Stephen, A tamely chaotic meta-Fibonacci sequence. Twenty-third Manitoba Conference on Numerical Mathematics and Computing (Winnipeg, MB, 1993). Congr. Numer. 99 (1994), 67-94. [Contains a detailed analysis of this sequence]
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..20000
Rémy Sigrist, Colored scatterplot of a(n) for n = 0..20000 (where the color is function of n mod 3)
Index entries for Hofstadter-type sequences
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MAPLE
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a:=proc(n) option remember; global k;
if n = 0 then 2
elif n = 1 then 1
elif n = 2 then 0
else
if (a(n-1) <= n-1) and (a(n-2) <= n-2) then
a(n-1-a(n-1))+a(n-2-a(n-2));
else lprint("died with n =", n); return (-1);
fi;
fi; end;
[seq(a(n), n=0..100)];
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PROG
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(Haskell)
a240808 n = a240808_list !! n
a240808_list = 2 : 1 : 0 : zipWith (+) xs (tail xs)
where xs = map a240808 $ zipWith (-) [1..] $ tail a240808_list
-- Reinhard Zumkeller, Apr 17 2014
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CROSSREFS
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A006949 and A240807 have the same recurrence but different initial conditions.
Trisections: A244780..A244782.
Sequence in context: A153247 A071432 A194508 * A263142 A025253 A281228
Adjacent sequences: A240805 A240806 A240807 * A240809 A240810 A240811
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KEYWORD
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nonn,look
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AUTHOR
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N. J. A. Sloane, Apr 15 2014
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STATUS
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approved
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