A247486 Numbers not achievable by the rules of 'Countdown' and 1,2,3,4,5,50.

766, 838, 842, 857, 858, 859, 861, 1073, 1087, 1091, 1093, 1094, 1106, 1107, 1108, 1109, 1112, 1114, 1117, 1118, 1123, 1132, 1138, 1142, 1154, 1157, 1163, 1174, 1178, 1223, 1226, 1258, 1262, 1268, 1273, 1276, 1277, 1278, 1281, 1282, 1283, 1286, 1289, 1291

Offset

1,1

Comments

The rules allow one to use +, -, *, /, the given numbers and parentheses. Not all numbers need to be used. A number can be used only once. Fractions are not allowed as intermediate results.

9000 = (1 + 2)*3*4*5*50 is the largest term missing. - Charles R Greathouse IV, Sep 19 2014

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Wikipedia, Countdown rules for numbers round

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = n + 2359 for n >= 6642. - Alois P. Heinz, Sep 22 2014

Example

The examples show some achievable numbers.  They are not listed by a:
5 * (3 + 1) - 4 = 5 * 3 + 1 = 16.
(50 - (1 + 2) * 3) * (4 + 5) = 41 * 9 = 369.
(2 * 4) * (50 - 3 - 1) + 5 = 373.
((50 - 2) * 4 + 1) * 3 - 5 = 574.
(1 + 3 * 4) * (50 + 2) - 5 = 671.

Maple

with(combinat):
l:= permute([1, 2, 3, 4, 5, 50]):
b:= proc(i, j, p) option remember; global l; `if`(i=j, l[p][j],
      select(x->x<>0 and is(x, integer), {seq(seq(seq([f+g, f-g,
      f*g, f/g][], g=b(k+1, j, p)), f=b(i, k, p)), k=i..j-1)}))
    end:
l:= sort([({$1..9000} minus {seq({seq(select(x->x>0,
    b(1, t, p))[], t=2..6)}[], p=1..6!)})[]]):
a:= n-> `if`(n<=6641, l[n], n+2359):
seq(a(n), n=1..100);  # Alois P. Heinz, Sep 22 2014

Crossrefs

Sequence in context: A127206 A343704 A343705 * A125109 A234163 A159209

Adjacent sequences: A247483 A247484 A247485 * A247487 A247488 A247489

Keyword

nonn,easy

Author

Jon Perry, Sep 18 2014

Extensions

More terms from Alois P. Heinz, Sep 22 2014

Status

approved