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A005379 The male of a pair of recurrences.
(Formerly M0278)
7

%I M0278

%S 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,

%T 17,18,19,19,20,20,21,22,22,23,24,24,25,25,26,27,27,28,29,29,30,30,31,

%U 32,32,33,33,34,35,35,36,37,37,38,38,39,40,40,41,42,42,43,43,44,45,45

%N The male of a pair of recurrences.

%C 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]

%D D. R. Hofstadter, "Goedel, Escher, Bach", p. 137.

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

%H Reinhard Zumkeller, <a href="/A005379/b005379.txt">Table of n, a(n) for n = 0..10000</a>

%H D. R. Hofstadter, <a href="/A006336/a006336_1.pdf">Eta-Lore</a> [Cached copy, with permission]

%H D. R. Hofstadter, <a href="/A006336/a006336_2.pdf">Pi-Mu Sequences</a> [Cached copy, with permission]

%H D. R. Hofstadter and N. J. A. Sloane, <a href="/A006336/a006336.pdf">Correspondence, 1977 and 1991</a>

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, 1992.

%H Th. Stoll, <a href="http://www.fq.math.ca/Papers1/46_47-1/Stoll_11-08.pdf">On Hofstadter's married functions</a>, Fib. Q., 46/47 (2008/2009), 62-67. - from _N. J. A. Sloane_, May 30 2009

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HofstadterMale-FemaleSequences.html">Hofstadter Male-Female Sequences.</a>

%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>

%H <a href="/index/Go#GEB">Index entries for sequences from "Goedel, Escher, Bach"</a>

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

%F 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

%p F:= proc(n) option remember; n - M(procname(n-1)) end proc:

%p M:= proc(n) option remember; n - F(procname(n-1)) end proc:

%p F(0):= 1: M(0):= 0:

%p seq(M(n),n=0..100); # _Robert Israel_, Jun 15 2015

%t 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}]

%t (* _Jean-François Alcover_, Jul 27 2011 *)

%o (Haskell) Cf. A005378.

%o (PARI) f(n) = if(n<1, 1, n - m(f(n - 1)));

%o m(n) = if(n<1, 0, n - f(m(n - 1)));

%o for(n=0, 73, print1(m(n),", ")) \\ _Indranil Ghosh_, Apr 23 2017

%Y Cf. A005378.

%K nonn,nice,easy

%O 0,4

%A _N. J. A. Sloane_

%E More terms from _James A. Sellers_, Jul 12 2000

%E Comment corrected by _Jaroslav Krizek_, Dec 25 2011

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Last modified June 19 17:48 EDT 2019. Contains 324222 sequences. (Running on oeis4.)