A135558 -id:A135558 - cp's OEIS frontend

A135709 Not the sum of three distinct nonzero Fibonacci numbers.

1, 2, 3, 4, 5, 7, 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, 174, 175, 176, 177, 182, 184, 185

Offset: 1

N. J. A. Sloane, Mar 05 2008

nonn

R. J. Mathar, Table of n, a(n) for n = 1..1000
Colm Mulcahy, Additional Certainties, MAA, Feb 2008

Complement of A135558.

Cf. A179244, A111458.

# needs isA135558 from A135558
A135709 := proc(n)
    option remember;
    local a;
    if n = 1 then
        1;
    else
        for a from procname(n-1)+1 do
            if not isA135558(a) then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Sep 09 2015

With[{f=15},Complement[Range[Fibonacci[f]],Total/@Subsets[Fibonacci[ Range[ 2,f]],{3}]]] (* Harvey P. Dale, Sep 08 2019 *)

A160238 Numbers n such that n^2 can be expressed as the sum of three different nonzero Fibonacci numbers.

Original entry on oeis.org

3, 4, 5, 6, 7, 8, 9, 10, 12, 16, 17, 18, 20, 23, 24, 25, 32, 33, 35, 37, 40, 47, 57, 86, 112, 123, 139, 216, 322, 843, 1161, 1476, 2207, 3864, 4999, 5778, 15127, 39603, 103682, 271443, 710647, 1244196, 1860498, 4870847, 12752043

Offset: 1

Carmine Suriano, May 05 2009

nonn

There exist a proper subsequence b(i)of a(n): n=[1, 2, 8, 17, 21, 24, 25, 28,29, 30, 31, 32, 33, 34, ...] such that approximatively b(i+1)=b(i)*(1+phi) where phi is 1.618... is the golden ratio and the approximation holds as a limit when i goes to infinity. For such a subsequence b(i) we have the following formula for the corresponding term when squared b(i)*b(i)=Fib(4*i+1)+Fib(4*i-1)+Fib(3). In the previous example 4999=b(9).

			4999*4999=24990001=Fib(37)+Fib(35)+Fib(3)

Cf. A000045, A135709, A135558.

Inserted 4 (with 4^2=13+1+2), 6 (with 36=21+2+13), 12 (with 12^2=89+21+34) etc. Added "nonzero" to definition - R. J. Mathar, Oct 23 2010

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A135709 Not the sum of three distinct nonzero Fibonacci numbers.

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A160238 Numbers n such that n^2 can be expressed as the sum of three different nonzero Fibonacci numbers.

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