

A078405


Smallest positive integer than cannot be obtained from exactly n copies of n using parentheses and the operations +, , /, *, ^ and concatenation.


2




OFFSET

1,1


COMMENTS

Only the original numbers may be concatenated, not the results of arithmetic operations (but see A078413).
Sequence is infinite. There are a finite number of expressions including n copies of n and various arithmetic operations. Hence A078405(n) is defined for any n. There is a trivial upper bound: A078405(n) < (n1)! * 6^(n1).  Max Alekseyev, Apr 17 2005


LINKS

Table of n, a(n) for n=1..9.
Erich Friedman, Math Magic: Problem of the Month (December 1999) (Possible inspiration for this sequence)
Index entries for similar sequences


EXAMPLE

With three 3's one can form 1=(3/3)^3, 2=33/3, 3=3+33, 4=3+3/3, but not 5, so a(3)=5.
With four 4's one can get 1=44/44, 2=4/4+4/4, 3=4(4/4)^4, 4=4+(44)^4, 5=4+(4/4)^4, 6=(4+4)/4+4, 7=44/44, 8=4+4+44, 9=4+4+4/4, 10=(444)/4, but not 11, so a(4)=11.


CROSSREFS

Cf. A078413.
Sequence in context: A208864 A259828 A104080 * A109278 A112527 A216642
Adjacent sequences: A078402 A078403 A078404 * A078406 A078407 A078408


KEYWORD

nonn,base


AUTHOR

Kit Vongmahadlek (kit119(AT)yahoo.com), Dec 27 2002


EXTENSIONS

a(7), a(8) and a(9) computed by Joseph DeVincentis (devjoe(AT)yahoo.com), Dec 27 2002


STATUS

approved



