A171745 - OEIS

%I #19 Nov 03 2019 01:41:43

%S 26,38,39,41,42,43,45,46,50,51,53,54,55,57,58,70,71,73,74,75,77,78,82,

%T 83,85,86,87,89,90,91,93,94,95,97,98,99,101,102,103,104,105,106,107,

%U 109,110,111,113,114,115,117,118,119,121,122,123,125,126,130,131,133

%N Nonnegative integers that cannot be obtained using six or fewer 4's with any combination of addition, subtraction, multiplication, or division.

%C Derived from the Numbers game from the British game show Countdown.

%H DataGenetics blog, <a href="http://datagenetics.com/blog/august32014/index.html">Countdown's Numbers Game</a>

%e 1 = 4 / 4

%e 2 = (4 + 4) / 4

%e 3 = 4 - (4 / 4)

%e ... ...

%e 25 = (4 * 4) + 4 + 4 + (4 / 4)

%e 26 cannot be solved

%e 27 = ((4 + 4) * 4) - 4 - (4 / 4)

%t 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 *)

%K nonn

%O 1,1

%A Hong Shao Yang (hongsy2006(AT)gmail.com), Dec 17 2009

%E More terms from _Giovanni Resta_, Nov 01 2019