A060274 Hard numbers: a(n) = smallest positive number m with f(m) = n, where f(m) is the smallest number of digits that are needed to construct m using only 1's, 2's and any number of +, -, *, ^ signs, not allowing concatenation of the digits.

1, 3, 5, 7, 13, 21, 41, 91, 269, 419, 921, 2983, 8519, 18859, 53611, 136631, 436341

Offset: 1

Author

Jason Earls, Mar 22 2001

Keywords

• nonn

Comments

It seems that to obtain this sequence we need to impose the additional rule that x-y is allowed only when x-y > 0.

This is not correct. See the comment at A099053. - Franklin T. Adams-Watters, Feb 14 2013

Examples

			a(11) = 921 because this is the smallest number that requires 11 digits for its expression.
		

References

• C. A. Pickover, "Wonders of Numbers", Chapter 78, 'Creator Numbers', Oxford University Press, NY, 2001. pp. 187-189, 343-345.
• Ken Shirriff, University of California, personal communication.

Links

• Sean A. Irvine, Java program (github)
• C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
• Index to sequences related to the complexity of n

Crossrefs

The sequence f(n) is given in A099053. Cf. A060273.

Extensions

Entry revised by Larry Reeves (larryr(AT)acm.org), Apr 26 2001

Entry improved by comments from Tim Peters (tim.one(AT)comcast.net), Nov 14 2004

a(17) from Sean A. Irvine, Nov 06 2022