A244750 - OEIS

%I #21 Dec 21 2024 02:00:41

%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 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 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,more

%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