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A111458 Numbers that cannot be represented as the sum of at most three Fibonacci numbers (with repetitions allowed). 4
33, 46, 51, 53, 54, 67, 72, 74, 75, 80, 82, 83, 85, 86, 87, 88, 101, 106, 108, 109, 114, 116, 117, 119, 120, 121, 122, 127, 129, 130, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 156, 161, 163, 164, 169, 171, 172 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
33 is neither a Fibonacci number nor can be written as the sum of two or three Fibonacci numbers.
MAPLE
isA111458 := proc(n) # returns true if n is in the sequence
local xi, yi, x, y, z ;
for xi from 0 do
x := A000045(xi) ;
if 3*x > n then
return true;
end if;
for yi from xi do
y := A000045(yi) ;
if x+2*y > n then
break;
else
z := n-x-y ;
if isA000045(z) then # see isFib in A000045
return false;
end if;
end if;
end do:
end do:
end proc:
A111458 := proc(n)
option remember;
local a;
if n = 0 then
-1;
else
for a from procname(n-1)+1 do
if isA111458(a) then
return a;
end if;
end do:
end if;
end proc: # R. J. Mathar, Sep 09 2015
MATHEMATICA
FibQ[n_] := IntegerQ[Sqrt[5n^2+4]] || IntegerQ[Sqrt[5n^2-4]];
P[n_] := IntegerPartitions[n, 3, Select[Range[n], FibQ]];
Select[Range[1000], P[#] == {}&] (* Jean-François Alcover, Jul 20 2023 *)
CROSSREFS
Sequence in context: A070121 A070122 A247527 * A179244 A258698 A258697
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified April 12 22:48 EDT 2024. Contains 371639 sequences. (Running on oeis4.)