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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 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 A296109 A102276 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 July 10 05:51 EDT 2020. Contains 335572 sequences. (Running on oeis4.)