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A258069 Nonnegative integers that can be computed using exactly eight 8's and the four basic arithmetic operations {+, -, *, /}.

%I A258069 #13 Nov 26 2018 14:36:45
%S A258069 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
%T A258069 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
%U A258069 49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,92
%N A258069 Nonnegative integers that can be computed using exactly eight 8's and the four basic arithmetic operations {+, -, *, /}.
%C A258069 The smallest non-computable number here is 91. The largest computable number here is 8^8 = 16777216.
%H A258069 Alois P. Heinz, <a href="/A258069/b258069.txt">Table of n, a(n) for n = 1..1660</a>
%p A258069 f:= proc(n) f(n):= `if`(n=1, {8}, {seq(seq(seq([x+y, x-y, x*y,
%p A258069       `if`(y=0, [][], x/y)][], y=f(n-j)), x=f(j)), j=1..n-1)})
%p A258069     end:
%p A258069 sort([select(z->z>=0 and is(z, integer), f(8))[]])[];
%o A258069 (PARI) A258069(n=8, S=Vec([[n]], n))={for(n=2, n, S[n]=Set(concat(vector(n\2, k, Set(concat([Set(concat([[T+U, T-U, U-T, if(U, T/U), if(T, U/T), T*U] | T <- S[n-k]])) | U <- S[k]])))))); select(t->t>=0 && type(t)=="t_INT", S[n])} \\ A258069() yields this sequence, use optional arg to compute variants. - _M. F. Hasler_, Nov 24 2018
%Y A258069 Cf. A171826, A171827, A171828, A171829, A258068, A258070, A258071.
%Y A258069 Cf. A182002, A258097.
%K A258069 nonn,fini,full
%O A258069 1,3
%A A258069 _Alois P. Heinz_, May 18 2015