

A005378


The female of a pair of recurrences.
(Formerly M0263)


8



1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 30, 31, 32, 32, 33, 34, 34, 35, 35, 36, 37, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 43, 44, 45, 45
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OFFSET

0,3


COMMENTS

The g.f. (1+z**2+z**4z**5+z**6)/(z**4+z**3+z**2+z+1)/(z1)**2 conjectured by Simon Plouffe in his 1992 dissertation is wrong.
F(n) is not equal to M(n) if and only if n+1 is a Fibonacci number (A000045); a(n)=A005379(n)+A192687(n). [Reinhard Zumkeller, Jul 12 2011]
Differs from A098294 in indices n=0,17,20,22,25,27,29,30,...  M. F. Hasler, Jun 29 2014


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).


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
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, 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) = nM(F(n1)); M(n) = nF(M(n1)).


MATHEMATICA

f[0] = 1; m[0] = 0; f[n_] := f[n] = n  m[f[n1]]; m[n_] := m[n] = n  f[m[n1]]; Table[f[n], {n, 0, 73}] (* JeanFrançois Alcover, Jul 27 2011 *)


PROG

(Haskell)
a005378 n = a005378_list !! n
a005378_list = 1 : zipWith () [1..] (map a005379 a005378_list)
a005379 n = a005379_list !! n
a005379_list = 0 : zipWith () [1..] (map a005378 a005379_list)
 Without memoization the original recursion would be feasible only for small n.
 Reinhard Zumkeller, Jul 12 2011


CROSSREFS

Cf. A005379.
Sequence in context: A098294 A195119 A077467 * A247911 A103355 A029092
Adjacent sequences: A005375 A005376 A005377 * A005379 A005380 A005381


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



