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A062877 Apart from the initial term (0), each a(n) is representable as a sum of distinct odd-indexed Fibonacci numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
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

E.g. 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 *)

CROSSREFS

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

A036796(n) - 1.

Sequence in context: A151894 A028229 A104452 * A068526 A287339 A039086

Adjacent sequences:  A062874 A062875 A062876 * A062878 A062879 A062880

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 26 2001

STATUS

approved

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Last modified October 22 15:11 EDT 2018. Contains 316490 sequences. (Running on oeis4.)