A078405 - OEIS

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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

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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: A104080 A375317 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