

A060274


Hard numbers: a(n) = smallest 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.


2



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

1,2


COMMENTS

It seems that to obtain this sequence we need to impose the additional rule that xy is allowed only when xy > 0.
This is not correct. See the comment at A099053.  Franklin T. AdamsWatters, Feb 14 2013


REFERENCES

C. A. Pickover, "Wonders of Numbers", Chapter 78, 'Creator Numbers', Oxford University Press, NY, 2001. pp. 187189, 343345.
Ken Shirriff, University of California, personal communication.


LINKS

Table of n, a(n) for n=1..16.
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: A180450 A051507 A173145 * A005235 A107664 A321671
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


STATUS

approved



