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

1,2

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

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

Table of n, a(n) for n=1..17.

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

Example

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

Crossrefs

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

Sequence in context: A051507 A173145 A347834 * A345130 A005235 A353284

Adjacent sequences: A060271 A060272 A060273 * A060275 A060276 A060277

Keyword

nonn

Author

Jason Earls, Mar 22 2001

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

Status

approved