A064818 Exotic numbers: write n in base 10 as d_1 d_2 ... d_k; sequence gives numbers n which can be obtained by using the digits d_1 ... d_k exactly once, at most one each of the symbols +, -, x, "divided by", sqrt, factorial, ^, together with any number of parentheses.

1, 2, 24, 25, 36, 64, 71

Offset: 1

Author

N. J. A. Sloane, Oct 23 2001

Keywords

• nonn
• base
• nice
• more

Comments

The trivial representation n = d_1 d_2 ... d_k is excluded.

I've found some more terms: 36 = 3!*6, 64 = sqrt(4)^6, 125 = 5^(1+2), 216 = 6^(1+2). But I haven't done an exhaustive search, so I'm not sure what a(5) is. There could be a term between 25 and 36. - David Wasserman, Aug 20 2002

From D. S. McNeil, Sep 07 2010: Probably the sequence up to 1000 is [1, 2, 24, 25, 36, 64, 71, 120, 121, 125, 126, 127, 128, 153, 184, 216, 289, 324, 337, 343, 347, 354, 355, 360, 384, 456, 464, 624, 625, 648, 660, 688, 693, 720, 729, 736], with about 10% chance of error.

Examples

			24 = (2+sqrt(4))!.
Alternatively, 24 = sqrt((4!)^2). - _David S. Johnson_
		

References

• Bernardo Recamán Santos, Challenging Brainteasers, Sterling, NY, 2000.

Links

• Michael S. Branicky, Representations for McNeil's terms < 1000

Extensions

The reference also gives 121 = 11^2, 127 = 2^7 - 1, 128 = 2^(8-1), 144 = (1+4)! + 4!, but missed 120 = (10/2)! found by Peter Shor.

a(5)-a(7) from D. S. McNeil, Sep 07 2010