A362471 a(n) is the smallest number of 1's used in expressing n as a calculation containing only decimal repunits and operators +, -, * and /.
1, 2, 3, 4, 5, 5, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 7, 6, 6, 5, 5, 4, 5, 5, 6, 6, 7, 7, 7, 6, 7, 6, 5, 6, 7, 6, 6, 7, 7, 7, 8, 7, 7, 6, 7, 7, 8, 7, 8, 7, 8, 8, 8, 7, 6, 6, 7, 8, 8, 7, 7, 8, 8, 8, 8, 7, 8, 8, 8, 9, 9, 8, 9, 8, 9, 9, 8, 8, 9, 8, 8, 9, 10, 9, 9, 9, 8, 7, 7
Offset: 1
Examples
For n = 6, 6 = (1+1)*(1+1+1), so a(6) = 5. For n = 32, 32 = 11*(1+1+1)-1, so a(32) = 6. For n = 37, 37 = 111/(1+1+1), so a(37) = 6. For n = 78, 78 = 111-(11)*(1+1+1), so a(78) = 8.
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10000
Formula
a(n+1) <= a(n) + 1.
a(n) <= a(i) + a(j), for all i O j = n, for O = +, -, *, /.
Comments