cp's OEIS Frontend

A171829 Nonnegative integers that can be made by using six sixes (6 6's) and the four basic operators {+, -, *, /}.

%I A171829 #38 Oct 12 2024 02:00:37
%S A171829 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,27,
%T A171829 28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,47,48,49,54,60,
%U A171829 65,66,67,69,70,71,72,73,74,75,77,78,79,84,90,96,102,107
%N A171829 Nonnegative integers that can be made by using six sixes (6 6's) and the four basic operators {+, -, *, /}.
%C A171829 More integers can be made if other operators are allowed (i.e., 22 = 6!/(6*6)+(6+6)/6). The sequence is finite: a(198) = 6*6*6*6*6*6 = 46656 is the last term.
%C A171829 See A258068 ff. for the integers that can be generated with the four basic operators and 7 7's, 8 8's, 9 9's, etc...
%H A171829 Alois P. Heinz, <a href="/A171829/b171829.txt">Table of n, a(n) for n = 1..198</a>
%H A171829 Wikipedia, <a href="http://en.wikipedia.org/wiki/Four_fours">Four Fours</a>
%e A171829 49 is in the sequence: 49 = (6 + 6/6) * (6 + 6/6).
%p A171829 f:= proc(n) f(n):= `if`(n=1, {6}, {seq(seq(seq([x+y, x-y, x*y,
%p A171829       `if`(y=0, [][], x/y)][], y=f(n-j)), x=f(j)), j=1..n-1)})
%p A171829     end:
%p A171829 sort([select(z->z>=0 and is(z, integer), f(6))[]])[];
%p A171829 #  _Alois P. Heinz_, Aug 04 2013
%t A171829 f[1] = {6}; f[n_] := f[n] = Union @ Flatten @ Table[Table[Table[{x+y, x-y, x*y, If[y == 0, Null, x/y]}, {y, f[n-j]}], {x, f[j]}], {j, 1, n-1}];
%t A171829 Sort[Select[f[6], # >= 0 && IntegerQ[#]&]] (* _Jean-François Alcover_, Jun 01 2018, after _Alois P. Heinz_ *)
%o A171829 (PARI) A171829(n=6, S=Vec([[n]],n))={for(n=2, n, S[n]=Set(concat(vector(n\2, k, concat([concat([[T+U, T-U, U-T, if(U, T/U), if(T, U/T), T*U] | T <- S[k]]) | U <- S[n-k]]))))); select(t-> t>=0 && denominator(t)==1,S[n])} \\ A171829() yields this sequence. Optional args allow to compute variants. - _M. F. Hasler_, Nov 24 2018
%Y A171829 Cf. A171826, A171827, A171828, A258068, A258069, A258070, A258071.
%Y A171829 Cf. A182002, A258097.
%K A171829 nonn,fini,full
%O A171829 1,3
%A A171829 _Sergio Pimentel_, Dec 19 2009
%E A171829 Corrected and edited by _Alois P. Heinz_, Aug 03 2013