A062877 0 and numbers representable as a sum of distinct odd-indexed Fibonacci numbers.

0, 1, 2, 3, 5, 6, 7, 8, 13, 14, 15, 16, 18, 19, 20, 21, 34, 35, 36, 37, 39, 40, 41, 42, 47, 48, 49, 50, 52, 53, 54, 55, 89, 90, 91, 92, 94, 95, 96, 97, 102, 103, 104, 105, 107, 108, 109, 110, 123, 124, 125, 126, 128, 129, 130, 131, 136, 137, 138, 139, 141, 142, 143, 144

Offset

0,3

Links

R. J. Mathar, Table of n, a(n) for n = 0..3071

A. Karttunen, On Pascal's Triangle Modulo 2 in Fibonacci Representation, The Fibonacci Quarterly, Vol. 42, #1 (2004) pp. 38-46.

Example

F_1 = 1,
F_3 = 2,
F_1 + F_3 = 3,
F_5 = 5,
F_5 + F_1 = 6,
F_5 + F_3 = 7,
F_5 + F_3 + F_1 = 8,
F_7 = 13, ...

Maple

with(combinat); [seq(A062877(j), j=0..265)]; A062877 := n -> add((floor(n/(2^i)) mod 2)*fibonacci((2*i)+1), i=0..floor_log_2(n+1));
floor_log_2 := proc(n) local nn, i; nn := n; for i from -1 to n do if(0 = nn) then RETURN(i); fi; nn := floor(nn/2); od; end;
# alternative
isA062877 := proc(n)
    local fset, fidx, ps ;
    if n = 0 then
        return true;
    end if;
    fset := {} ;
    for fidx from 1 by 2 do
        if combinat[fibonacci](fidx) >n then
            break;
        end if;
        fset := fset union {combinat[fibonacci](fidx)} ;
    end do:
    for ps in combinat[powerset](fset) do
        if n = add(fidx, fidx=ps) then
            return true;
        end if;
    end do:
    return false;
end proc: # R. J. Mathar, Aug 22 2016

Mathematica

Take[Union[Total/@Subsets[Fibonacci[Range[1, 20, 2]]]], 70](* Harvey P. Dale, Dec 21 2013 *)

Prog

(PARI) my(m=Mod('x, 'x^2-3*'x+1)); a(n) = subst(lift(subst(Pol(binary(n)), 'x, m)), 'x, 2); \\ Kevin Ryde, Nov 25 2020

Crossrefs

A062878 gives the positions of A050614(n) in this sequence. A062879 is bisection.

A036796(n) - 1.

Cf. A022290 (even-indexed Fibonaccis), A054204.

Sequence in context: A104452 A335073 A344514 * A068526 A287339 A039086

Adjacent sequences: A062874 A062875 A062876 * A062878 A062879 A062880

Keyword

nonn

Author

Antti Karttunen, Jun 26 2001

Status

approved