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A005379 The male of a pair of recurrences.
(Formerly M0278)
7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

M(n) is not equal to F(n) if and only if n+1 is a Fibonacci number (A000045); a(n)=A005379(n)-A192687(n). [Reinhard Zumkeller, Jul 12 2011]

REFERENCES

Hofstadter, "Goedel, Escher, Bach", p. 137.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Th. Stoll, On Hofstadter's married functions, Fib. Q., 46/47 (2008/2009), 62-67. - from N. J. A. Sloane, May 30 2009

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

D. R. Hofstadter, Eta-Lore [Cached copy, with permission]

D. R. Hofstadter, Pi-Mu Sequences [Cached copy, with permission]

D. R. Hofstadter and N. J. A. Sloane, Correspondence, 1977 and 1991

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Eric Weisstein's World of Mathematics, Hofstadter Male-Female Sequences.

Index entries for Hofstadter-type sequences

Index entries for sequences from "Goedel, Escher, Bach"

FORMULA

F(0) = 1; M(0) = 0; F(n) = n-M(F(n-1)); M(n) = n-F(M(n-1)).

MAPLE

A005379:=-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.]

This conjecture is false; the coefficient of z^33 in the g.f. is 21, but A005379(33) = 20. (Discovered by Sahand Saba, Jan 14 2013.) -  Frank Ruskey, Jan 16 2013

MATHEMATICA

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}]

(* Jean-François Alcover, Jul 27 2011 *)

PROG

(Haskell) Cf. A005378.

CROSSREFS

Cf. A005378.

Sequence in context: A078489 A194179 A101803 * A029922 A020915 A156301

Adjacent sequences:  A005376 A005377 A005378 * A005380 A005381 A005382

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from James A. Sellers, Jul 12 2000.

Comment corrected by Jaroslav Krizek, Dec 25 2011.

STATUS

approved

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Last modified December 19 22:28 EST 2014. Contains 252240 sequences.