A171745 Nonnegative integers that cannot be obtained using six or fewer 4's with any combination of addition, subtraction, multiplication, or division.

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..60.

DataGenetics blog, Countdown's Numbers Game

Example

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)

Mathematica

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 *)

Crossrefs

Sequence in context: A034106 A239604 A213012 * A045092 A106551 A106553

Adjacent sequences: A171742 A171743 A171744 * A171746 A171747 A171748

Keyword

nonn

Author

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

Extensions

More terms from Giovanni Resta, Nov 01 2019

Status

approved