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A005379
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The male of a pair of recurrences.
(Formerly M0278)
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8
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0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 30, 31, 32, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 43, 44, 45, 45
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listen;
history;
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OFFSET
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0,4
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COMMENTS
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REFERENCES
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D. R. 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)).
The g.f. -z^2*(-1-z^3-z^6-z-z^4-z^7+z^8)/(z+1)/(z^2+1)/(z^4+1)/(z-1)^2, conjectured by Simon Plouffe in his 1992 dissertation is incorrect: the coefficient of z^33 in the g.f. is 21, but a(33) = 20. (Discovered by Sahand Saba, Jan 14 2013.) - Frank Ruskey, Jan 16 2013
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MAPLE
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F:= proc(n) option remember; n - M(procname(n-1)) end proc:
M:= proc(n) option remember; n - F(procname(n-1)) end proc:
F(0):= 1: M(0):= 0:
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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[m[n], {n, 0, 73}]
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PROG
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(PARI) f(n) = if(n<1, 1, n - m(f(n - 1)));
m(n) = if(n<1, 0, n - f(m(n - 1)));
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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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