

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
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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, fg,
f*g, f/g][], g=b(k+1, j, p)), f=b(i, k, p)), k=i..j1)}))
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



