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 A019586 Vertical para-Fibonacci sequence: takes value i on later (i.e., b_j, j >= 2) terms of i-th 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 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=1..87. 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 Equals A003603(n) - 1. Cf. Wythoff array: A035513. Sequence in context: A025648 A025655 A022336 * A257962 A176095 A295508 Adjacent sequences: A019583 A019584 A019585 * A019587 A019588 A019589 KEYWORD nonn,nice,easy,eigen AUTHOR N. J. A. Sloane and J. H. Conway 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

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Last modified June 6 10:50 EDT 2023. Contains 363142 sequences. (Running on oeis4.)