A179244 -id:A179244 - cp's OEIS frontend

A179252 Numbers that have 12 terms in their Zeckendorf representation.

75024, 103681, 114627, 118808, 120405, 121015, 121248, 121337, 121371, 121384, 121389, 121391, 121392, 150049, 160995, 165176, 166773, 167383, 167616, 167705, 167739, 167752, 167757, 167759, 167760, 178706, 182887, 184484, 185094, 185327, 185416, 185450, 185463

Offset: 1

Emeric Deutsch, Jul 05 2010

nonn

			75024 = 1 + 3 + 8 + 21 + 55 + 144 + 377 + 987 + 2584 + 6765 + 17711 + 46368;
103681 = 1 + 3 + 8 + 21 + 55 + 144 + 377 + 987 + 2584 + 6765 + 17711 + 75025.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000045, A035517, A007895, A179242, A179243, A179244, A179245, A179246, A179247, A179248, A179249, A179250, A179251, A179253.

with(combinat): B := proc (n) local A, ct, m, j: A := proc (n) local i: for i while fibonacci(i) <= n do n-fibonacci(i) end do end proc: ct := 0: m := n: for j while 0 < A(m) do ct := ct+1: m := A(m) end do: ct+1 end proc: Q := {}: for i from fibonacci(25)-1 to 180000 do if B(i) = 12 then Q := `union`(Q, {i}) else end if end do: Q;

Reap[For[m = 0; k = 1, k <= 10^8, k++, If[BitAnd[k, 2 k] == 0, m++; If[DigitCount[k, 2, 1] == 12, Print[m]; Sow[m]]]]][[2, 1]] (* Jean-François Alcover, Aug 20 2023 *)

A135709 Not the sum of three distinct nonzero Fibonacci numbers.

Original entry on oeis.org

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 *)

A111458 Numbers that cannot be represented as the sum of at most three Fibonacci numbers (with repetitions allowed).

Original entry on oeis.org

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

Offset: 1

Stefan Steinerberger, Nov 15 2005

nonn

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

R. J. Mathar, Table of n, a(n) for n = 1..1000

Cf. A000045, A000119, A179244, A135709.

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

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 *)

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A179252 Numbers that have 12 terms in their Zeckendorf representation.

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A135709 Not the sum of three distinct nonzero Fibonacci numbers.

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Maple

Mathematica

A111458 Numbers that cannot be represented as the sum of at most three Fibonacci numbers (with repetitions allowed).

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Maple

Mathematica