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%I #17 Jul 13 2014 00:20:39
%S 0,2,3,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,
%T 131072,262144
%N 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}.
%D R. K. Guy, "s-Additive sequences," preprint, 1994.
%H S. R. Finch, <a href="http://www.jstor.org/stable/2325001">Are 0-additive sequences always regular?</a>, Amer. Math. Monthly, 99 (1992), 671-673.
%e a(5) cannot be 5=2+3. It cannot be 6=2+4. It cannot be 7=3+4, and becomes a(5)=8.
%e 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.
%p A244750:= proc(n)
%p option remember;
%p if n <= 4 then
%p op(n,[0,2,3,4]);
%p else
%p prev := {seq(procname(k),k=1..n-1)} ;
%p for a from procname(n-1)+1 do
%p awrks := true ;
%p for asub in combinat[choose](prev) do
%p if add(p,p=asub) = a then
%p awrks := false;
%p break;
%p end if;
%p end do:
%p if awrks then
%p return a;
%p end if;
%p end do:
%p end if;
%p end proc:
%p for n from 1 do
%p print(A244750(n)) ;
%p end do: # _R. J. Mathar_, Jul 12 2014
%t 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]
%Y Cf. A003662, A003663, A005408, A026471, A026474, A033627, A051039, A051040, A244151, A244749.
%Y Cf. A060469, A060470, A060471, A060472.
%K nonn
%O 1,2
%A _N. J. A. Sloane_ and _Robert G. Wilson v_, Jul 05 2014
%E Corrected by _R. J. Mathar_, Jul 12 2014
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