OFFSET
0,3
COMMENTS
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 at 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
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
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.
FORMULA
F(0) = 1; M(0) = 0; F(n) = n-M(F(n-1)); M(n) = n-F(M(n-1)).
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[f[n], {n, 0, 73}] (* Jean-François 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
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Jul 12 2000
Comment corrected by Jaroslav Krizek, Dec 25 2011
STATUS
approved