cp's OEIS Frontend

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

%I A106530 #27 Feb 16 2025 08:32:57
%S A106530 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,
%T A106530 105,105,210,168,168,168,168,168,34,34,34,102,102,170,170,170,136,136,
%U A106530 136,408,408,442,442,442,1326,1326,2210,2210,2210,55,55,110,165,165,55,55,110,440,440
%N A106530 Least common multiple of all parts in Zeckendorf representation of n.
%C A106530 Records: A106531(n) = a(A106532(n)).
%C A106530 a(n) = lcm_{k=0..A007895(n)-1} A035516(n,k). - _Reinhard Zumkeller_, Mar 10 2013
%H A106530 Alois P. Heinz, <a href="/A106530/b106530.txt">Table of n, a(n) for n = 1..16384</a> (first 10000 terms from Reinhard Zumkeller)
%H A106530 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ZeckendorfRepresentation.html">Zeckendorf Representation</a>
%H A106530 <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>.
%e A106530 n=33: 21+8+3+1 = 33 -> a(33) = lcm(21,8,3,1) = (21*8*3*1)/3 = 168.
%p A106530 F:= combinat[fibonacci]:
%p A106530 a:= proc(n) option remember; local j;
%p A106530       if n=0 then 1
%p A106530     else for j from 2 while F(j+1)<=n do od;
%p A106530          ilcm(a(n-F(j)), F(j))
%p A106530       fi
%p A106530     end:
%p A106530 seq(a(n), n=1..64);  # _Alois P. Heinz_, Mar 17 2018
%t A106530 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 *)
%o A106530 (Haskell)
%o A106530 a106530 = foldr lcm 1 . a035516_row -- _Reinhard Zumkeller_, Mar 10 2013
%Y A106530 Cf. A000045, A014417, A003714.
%K A106530 nonn,look
%O A106530 1,2
%A A106530 _Reinhard Zumkeller_, May 08 2005