A171827 Nonnegative integers that can be made by using exactly four fours (4 4's) and the four basic operators {+, -, *, /}.

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

Offset: 1

Author

Sergio Pimentel, Dec 19 2009

Keywords

• nonn
• fini
• full

Comments

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.

Examples

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

Links

• Wikipedia, Four Fours

Crossrefs

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

Cf. A182002, A258097.

Programs

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