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A244750 0-additive sequence: a(n) is the smallest number larger than a(n-1) which is not the sum of any subset of earlier terms, with initial values {0, 2, 3, 4}. 2
0, 2, 3, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

R. K. Guy, "s-Additive sequences," preprint, 1994.

LINKS

Table of n, a(n) for n=1..20.

S. R. Finch, Are 0-additive sequences always regular?, Amer. Math. Monthly, 99 (1992), 671-673.

EXAMPLE

a(5) cannot be 5=2+3. It cannot be 6=2+4. It cannot be 7=3+4, and becomes a(5)=8.

a(6) cannot be 9=2+3+4. It cannot be 10=2+8. It cannot be 11=3+8. It cannot be 12 = 4+8. It cannot be 13=2+3+8. It cannot be 14=2+4+8. It cannot be 15=3+4+8, and becomes a(6)=16.

MAPLE

A244750:= proc(n)

    option remember;

    if n <= 4 then

        op(n, [0, 2, 3, 4]);

    else

        prev := {seq(procname(k), k=1..n-1)} ;

        for a from procname(n-1)+1 do

            awrks := true ;

            for asub in combinat[choose](prev) do

                if add(p, p=asub) = a then

                    awrks := false;

                    break;

                end if;

            end do:

            if awrks then

                return a;

            end if;

        end do:

    end if;

end proc:

for n from 1 do

    print(A244750(n)) ;

end do: # R. J. Mathar, Jul 12 2014

MATHEMATICA

f[s_List] := f[n] = Block[{k = s[[-1]] + 1, ss = Union[Plus @@@ Subsets[s]]}, While[ MemberQ[ss, k], k++]; Append[s, k]]; Nest[ f[#] &, {0, 2, 3, 4}, 16]

CROSSREFS

Cf. A003662, A003663, A005408, A026471, A026474, A033627, A051039, A051040, A244151, A244749.

Cf. A060469, A060470, A060471, A060472.

Sequence in context: A126294 A224912 A162724 * A140974 A118841 A296109

Adjacent sequences:  A244747 A244748 A244749 * A244751 A244752 A244753

KEYWORD

nonn

AUTHOR

N. J. A. Sloane and Robert G. Wilson v, Jul 05 2014

EXTENSIONS

Corrected by R. J. Mathar, Jul 12 2014

STATUS

approved

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Last modified June 16 19:43 EDT 2019. Contains 324155 sequences. (Running on oeis4.)