A106530 Least common multiple of all parts in Zeckendorf representation of n.

1, 2, 3, 3, 5, 5, 10, 8, 8, 8, 24, 24, 13, 13, 26, 39, 39, 65, 65, 130, 21, 21, 42, 21, 21, 105, 105, 210, 168, 168, 168, 168, 168, 34, 34, 34, 102, 102, 170, 170, 170, 136, 136, 136, 408, 408, 442, 442, 442, 1326, 1326, 2210, 2210, 2210, 55, 55, 110, 165, 165, 55, 55, 110, 440, 440

Offset

1,2

Comments

Records: A106531(n) = a(A106532(n)).

a(n) = lcm_{k=0..A007895(n)-1} A035516(n,k). - Reinhard Zumkeller, Mar 10 2013

Links

Alois P. Heinz, Table of n, a(n) for n = 1..16384 (first 10000 terms from Reinhard Zumkeller)

Eric Weisstein's World of Mathematics, Zeckendorf Representation

Index entries for sequences related to lcm's.

Example

n=33: 21+8+3+1 = 33 -> a(33) = lcm(21,8,3,1) = (21*8*3*1)/3 = 168.

Maple

F:= combinat[fibonacci]:
a:= proc(n) option remember; local j;
      if n=0 then 1
    else for j from 2 while F(j+1)<=n do od;
         ilcm(a(n-F(j)), F(j))
      fi
    end:
seq(a(n), n=1..64);  # Alois P. Heinz, Mar 17 2018

Mathematica

t = Fibonacci /@ Range@ 21; Table[LCM @@ If[MemberQ[t, n], {n}, Most@ MapAt[# + 1 &, Abs@ Differences@ FixedPointList[# - First@ Reverse@ TakeWhile[t, Function[k, # >= k]] &, n], -1]], {n, 61}] (* Michael De Vlieger, May 17 2016 *)

Prog

(Haskell)
a106530 = foldr lcm 1 . a035516_row -- Reinhard Zumkeller, Mar 10 2013

Crossrefs

Cf. A000045, A014417, A003714.

Sequence in context: A240176 A134408 A051032 * A273156 A294487 A212792

Adjacent sequences: A106527 A106528 A106529 * A106531 A106532 A106533

Keyword

nonn,look

Author

Reinhard Zumkeller, May 08 2005

Status

approved