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A005378
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The female of a pair of recurrences.
(Formerly M0263)
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8
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1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 30, 31, 32, 32, 33, 34, 34, 35, 35, 36, 37, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 43, 44, 45, 45
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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Differs from A098294 at indices n = 0, 17, 20, 22, 25, 27, 29, 30, ... - M. F. Hasler, Jun 29 2014
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REFERENCES
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Hofstadter, "Goedel, Escher, Bach", p. 137.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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D. R. Hofstadter, Eta-Lore [Cached copy, with permission]
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FORMULA
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F(0) = 1; M(0) = 0; F(n) = n-M(F(n-1)); M(n) = n-F(M(n-1)).
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MATHEMATICA
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f[0] = 1; m[0] = 0; f[n_] := f[n] = n - m[f[n-1]]; m[n_] := m[n] = n - f[m[n-1]]; Table[f[n], {n, 0, 73}] (* Jean-François Alcover, Jul 27 2011 *)
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PROG
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(Haskell)
a005378 n = a005378_list !! n
a005378_list = 1 : zipWith (-) [1..] (map a005379 a005378_list)
a005379 n = a005379_list !! n
a005379_list = 0 : zipWith (-) [1..] (map a005378 a005379_list)
-- Without memoization the original recursion would be feasible only for small n.
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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