A078413 -id:A078413 - cp's OEIS frontend

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

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

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

			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.

Erich Friedman, Math Magic: Problem of the Month (December 1999) (Possible inspiration for this sequence)
Index entries for similar sequences

Cf. A078413.

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

a(1)-a(9) verified by Sean A. Irvine, Jun 29 2025

cp's OEIS Frontend

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

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