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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}.

%I A244750 #21 Dec 21 2024 02:00:41
%S A244750 0,2,3,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,
%T A244750 131072,262144
%N 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}.
%D A244750 R. K. Guy, "s-Additive sequences," preprint, 1994.
%H A244750 Steven 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 A244750 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 A244750 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 A244750:= proc(n)
%p A244750     option remember;
%p A244750     if n <= 4 then
%p A244750         op(n,[0,2,3,4]);
%p A244750     else
%p A244750         prev := {seq(procname(k),k=1..n-1)} ;
%p A244750         for a from procname(n-1)+1 do
%p A244750             awrks := true ;
%p A244750             for asub in combinat[choose](prev) do
%p A244750                 if add(p,p=asub) = a then
%p A244750                     awrks := false;
%p A244750                     break;
%p A244750                 end if;
%p A244750             end do:
%p A244750             if awrks then
%p A244750                 return a;
%p A244750             end if;
%p A244750         end do:
%p A244750     end if;
%p A244750 end proc:
%p A244750 for n from 1 do
%p A244750     print(A244750(n)) ;
%p A244750 end do: # _R. J. Mathar_, Jul 12 2014
%t A244750  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 A244750 Cf. A003662, A003663, A005408, A026471, A026474, A033627, A051039, A051040, A244151, A244749.
%Y A244750 Cf. A060469, A060470, A060471, A060472.
%K A244750 nonn,more
%O A244750 1,2
%A A244750 _N. J. A. Sloane_ and _Robert G. Wilson v_, Jul 05 2014
%E A244750 Corrected by _R. J. Mathar_, Jul 12 2014