OFFSET
1,6
COMMENTS
Gives number of row in Wythoff array that contains n. - Casey Mongoven, Sep 10 2005
For a method of generating this sequence that does not refer to the Wythoff array or Fibonacci numbers, see A003603. - Clark Kimberling, Oct 29 2009
LINKS
J. H. Conway and N. J. A. Sloane, Notes on the Para-Fibonacci and related sequences
Casey Mongoven, Sonification of multiple Fibonacci-related sequences, Annales Mathematicae et Informaticae, 41 (2013) pp. 175-192.
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
N. J. A. Sloane, Classic Sequences
FORMULA
Says which row of Wythoff array (starting row count at 0) contains n.
If delete first occurrence of 0, 1, 2, 3, ... the sequence is unchanged.
MAPLE
A019586 := proc(n::posint)
local r, c, W ;
for r from 1 do
for c from 1 do
W := A035513(r, c) ;
if W = n then
return r-1 ;
elif W > n then
break ;
end if;
end do:
end do:
end proc:
seq(A019586(n), n=1..100) ; # R. J. Mathar, Aug 13 2021
MATHEMATICA
row[1] = row[2] = {1}; row[n_] := row[n] = Module[{ro, pos, lp, ins}, ro = row[n - 1]; pos = Position[ro, Alternatives @@ Intersection[ro, row[n - 2]]] // Flatten; lp = Length[pos]; ins = Range[lp] + Max[ro]; Do[ro = Insert[ro, ins[[i]], pos[[i]] + i], {i, 1, lp}]; ro];
Flatten[Array[row, 9] - 1] (* Jean-François Alcover, Jul 12 2016, after Clark Kimberling *)
CROSSREFS
KEYWORD
nonn,nice,easy,eigen
AUTHOR
EXTENSIONS
Casey Mongoven reports that where the sequence reads 15,9,2,16,10,6,29,1,30,11,7,19,..., the 29 and 30 should be 17 and 18.
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 29 2003
STATUS
approved