A005379 The male of a pair of recurrences.
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
Offset: 0
References
- 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).
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; arXiv:0911.4975 [math.NT], 2009.
- Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
- J. Shallit, Proving properties of some greedily-defined integer recurrences via automata theory, arXiv:2308.06544 [cs.DM], August 12 2023.
- Th. Stoll, On Hofstadter's married functions, Fib. Q., 46/47 (2008/2009), 62-67. - from _N. J. A. Sloane_, May 30 2009
- Eric Weisstein's World of Mathematics, Hofstadter Male-Female Sequences.
- Index entries for Hofstadter-type sequences
- Index entries for sequences from "Goedel, Escher, Bach"
Crossrefs
Cf. A005378.
Programs
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Haskell
Cf. A005378.
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Maple
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: seq(M(n),n=0..100); # Robert Israel, Jun 15 2015
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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 *) -
PARI
f(n) = if(n<1, 1, n - m(f(n - 1))); m(n) = if(n<1, 0, n - f(m(n - 1))); for(n=0, 73, print1(m(n),", ")) \\ Indranil Ghosh, Apr 23 2017
Formula
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
Extensions
More terms from James Sellers, Jul 12 2000
Comment corrected by Jaroslav Krizek, Dec 25 2011
Comments