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A244750
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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}.
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2
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0, 2, 3, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144
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OFFSET
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1,2
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REFERENCES
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R. K. Guy, "s-Additive sequences," preprint, 1994.
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LINKS
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EXAMPLE
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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.
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MAPLE
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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
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MATHEMATICA
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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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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