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A171745
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Nonnegative integers that cannot be obtained using six or fewer 4's with any combination of addition, subtraction, multiplication, or division.
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0
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26, 38, 39, 41, 42, 43, 45, 46, 50, 51, 53, 54, 55, 57, 58, 70, 71, 73, 74, 75, 77, 78, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 113, 114, 115, 117, 118, 119, 121, 122, 123, 125, 126, 130, 131, 133
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OFFSET
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1,1
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COMMENTS
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Derived from the Numbers game from the British game show Countdown.
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LINKS
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EXAMPLE
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1 = 4 / 4
2 = (4 + 4) / 4
3 = 4 - (4 / 4)
... ...
25 = (4 * 4) + 4 + 4 + (4 / 4)
26 cannot be solved
27 = ((4 + 4) * 4) - 4 - (4 / 4)
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MATHEMATICA
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ops = {Plus, Subtract, Times, Divide}; ex[w_] := Block[{s = {}}, Do[If[e==0, AppendTo[s, 4], s[[-2]] = Quiet[s[[-2]]~ops[[e]]~s[[-1]]]; s = Most[s]], {e, w}]; s[[1]]]; ric[w_, tg_, no_, n4_, trg_] := Block[{v}, If[tg == 0, v = ex[w]; If[Quiet[v >= 0 && IntegerQ[v]], Sow[v]], If[n4 < trg, ric[Append[w, 0], tg-1, no, n4+1, trg]]; If[no < n4-1, Do[ric[Append[w, j], tg-1, no+1, n4, trg], {j, 4}]]]]; do[n4_] := Union[Reap[ric[{}, 2*n4-1, 0, 0, n4]][[2, 1]]]; Complement[ Range[0, 150], Union @@ Array[do, 6]] (* Giovanni Resta, Nov 01 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Hong Shao Yang (hongsy2006(AT)gmail.com), Dec 17 2009
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EXTENSIONS
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STATUS
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approved
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