

A019586


Vertical paraFibonacci sequence: takes value i on later (i.e., b_j, j >= 2) terms of ith Fibonacci sequence defined by b_0 = i, b_1 = [ tau(i+1) ].


25



0, 0, 0, 1, 0, 2, 1, 0, 3, 2, 1, 4, 0, 5, 3, 2, 6, 1, 7, 4, 0, 8, 5, 3, 9, 2, 10, 6, 1, 11, 7, 4, 12, 0, 13, 8, 5, 14, 3, 15, 9, 2, 16, 10, 6, 17, 1, 18, 11, 7, 19, 4, 20, 12, 0, 21, 13, 8, 22, 5, 23, 14, 3, 24, 15, 9, 25, 2, 26, 16, 10, 27, 6, 28, 17, 1, 29, 18, 11, 30, 7, 31, 19, 4, 32, 20, 12
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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



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

local r, c, W ;
for r from 1 do
for c from 1 do
if W = n then
return r1 ;
elif W > n then
break ;
end if;
end do:
end do:
end proc:


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];


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



