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A247486 Numbers not achievable by the rules of 'Countdown' and 1,2,3,4,5,50. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A158126 A124413 A127206 * 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

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Last modified October 23 05:13 EDT 2018. Contains 316519 sequences. (Running on oeis4.)