A078405 Smallest positive integer than cannot be obtained from exactly n copies of n using parentheses and the operations +, -, /, *, ^ and concatenation.

2, 2, 5, 11, 18, 50, 131, 226, 438

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) < (n-1)! * 6^(n-1). - 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=3-3/3, 3=3+3-3, 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+(4-4)^4, 5=4+(4/4)^4, 6=(4+4)/4+4, 7=44/4-4, 8=4+4+4-4, 9=4+4+4/4, 10=(44-4)/4, but not 11, so a(4)=11.

Crossrefs

Cf. A078413.

Sequence in context: A366094 A104080 A336269 * A109278 A367966 A112527

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