A111458 - OEIS

%I #14 Jul 20 2023 07:21:04

%S 33,46,51,53,54,67,72,74,75,80,82,83,85,86,87,88,101,106,108,109,114,

%T 116,117,119,120,121,122,127,129,130,132,133,134,135,137,138,139,140,

%U 141,142,143,156,161,163,164,169,171,172

%N Numbers that cannot be represented as the sum of at most three Fibonacci numbers (with repetitions allowed).

%H R. J. Mathar, <a href="/A111458/b111458.txt">Table of n, a(n) for n = 1..1000</a>

%e 33 is neither a Fibonacci number nor can be written as the sum of two or three Fibonacci numbers.

%p isA111458 := proc(n) # returns true if n is in the sequence

%p     local xi,yi,x,y,z ;

%p     for xi from 0 do

%p         x := A000045(xi) ;

%p         if 3*x > n then

%p             return true;

%p         end if;

%p         for yi from xi do

%p             y := A000045(yi) ;

%p             if x+2*y > n then

%p                 break;

%p             else

%p                 z := n-x-y ;

%p                 if isA000045(z) then # see isFib in A000045

%p                     return false;

%p                 end if;

%p             end if;

%p         end do:

%p     end do:

%p end proc:

%p A111458 := proc(n)

%p     option remember;

%p     local a;

%p     if n = 0 then

%p         -1;

%p     else

%p         for a from procname(n-1)+1 do

%p             if isA111458(a) then

%p                 return a;

%p             end if;

%p         end do:

%p     end if;

%p end proc: # _R. J. Mathar_, Sep 09 2015

%t FibQ[n_] := IntegerQ[Sqrt[5n^2+4]] || IntegerQ[Sqrt[5n^2-4]];

%t P[n_] := IntegerPartitions[n, 3, Select[Range[n], FibQ]];

%t Select[Range[1000], P[#] == {}&] (* _Jean-François Alcover_, Jul 20 2023 *)

%Y Cf. A000045, A000119, A179244, A135709.

%K nonn

%O 1,1

%A _Stefan Steinerberger_, Nov 15 2005