A171827 - OEIS

%I #18 Nov 26 2018 14:34:47

%S 0,1,2,3,4,5,6,7,8,9,12,15,16,17,20,24,28,32,36,48,60,64,68,80,128,256

%N Nonnegative integers that can be made by using exactly four fours (4 4's) and the four basic operators {+, -, *, /}.

%C Every integer can be made if other operators are allowed (e.g., 14 = 4!/4 + 4 + 4). The sequence is finite: a(26) = 4*4*4*4=256 is the last term.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Four_fours">Four Fours</a>

%e Example: a(11) = 12 since 12 = (4 - 4/4) * 4.

%o (PARI) A171827(n=4, 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[n-k]]) | U <- S[k]]))))); [t|t <- S[n], t>=0 && type(t)=="t_INT"]} \\ A171827() yields this sequence, use optional arg to compute variants. - _M. F. Hasler_, Nov 24 2018

%Y Cf. A171826, A171828, A171829, A258068, A258069, A258070, A258071.

%Y Cf. A182002, A258097.

%K nonn,fini,full

%O 1,3

%A _Sergio Pimentel_, Dec 19 2009