

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
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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

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, EtaLore [Cached copy, with permission]
D. R. Hofstadter, PiMu 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.
Th. Stoll, On Hofstadter's married functions, Fib. Q., 46/47 (2008/2009), 6267.  from N. J. A. Sloane, May 30 2009
Eric Weisstein's World of Mathematics, Hofstadter MaleFemale Sequences.
Index entries for Hofstadtertype sequences
Index entries for sequences from "Goedel, Escher, Bach"


FORMULA

F(0) = 1; M(0) = 0; F(n) = n  M(F(n1)); M(n) = n  F(M(n1)).
The g.f. z^2*(1z^3z^6zz^4z^7+z^8)/(z+1)/(z^2+1)/(z^4+1)/(z1)^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


MAPLE

F:= proc(n) option remember; n  M(procname(n1)) end proc:
M:= proc(n) option remember; n  F(procname(n1)) end proc:
F(0):= 1: M(0):= 0:
seq(M(n), n=0..100); # Robert Israel, Jun 15 2015


MATHEMATICA

f[0] = 1; m[0] = 0; f[n_] := f[n] = n  m[f[n1]]; m[n_] := m[n] = n  f[m[n1]]; Table[m[n], {n, 0, 73}]
(* JeanFrançois 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



