A171826 Nonnegative integers that can be made using exactly three threes (3 3's) and the four basic operators {+, -, *, /}.

0, 2, 3, 4, 6, 9, 12, 18, 27

Offset: 1

Author

Sergio Pimentel, Dec 19 2009

Keywords

• nonn
• fini
• full

Comments

More integers can be made using 3 3's if more operators are allowed (i.e., 1 = 3^(3-3) or 5 = 3! - 3/3). Note that 1 = 3/3 but the sequence requires to use exactly three threes and it's not possible to "get rid" of the third three.

Examples

			a(1) = 0 = (3-3)*3, a(2) = 2 = 3 - 3/3, a(3) = 3 = 3*3/3,
a(4) = 4 = 3 + 3/3, a(5) = 6 = 3*3 - 3, a(6) = 9 = 3 + 3 + 3,
a(7) = 12 = 3*3 + 3, a(8) = 18 = (3+3)*3, a(9) = 27 = 3*3*3.
		

Links

• Wikipedia, Four Fours

Crossrefs

Cf. A171827, A171828, A171829, A258068, A258069, A258070, A258071 (analog for four 4's, ..., ten 10's).

Cf. A182002, A258097.

Programs

PARI

vecextract([0..27],134484573) \\ Better programs to compute this are available in the related sequences, but they are much longer than this sequence itself. - M. F. Hasler, Nov 24 2018