A370829 Minimum number of (-1)'s needed to write n, using +, *, ^ and parentheses, disallowing noninteger intermediate values.
2, 3, 4, 4, 6, 5, 7, 6, 6, 7, 8, 7, 9, 8, 7, 6, 8, 9, 10, 9, 10, 11, 10, 9, 8, 9, 8, 9, 10, 10, 10, 9, 10, 10, 9, 8, 10, 11, 11, 11, 13, 12, 13, 12, 11, 12, 11, 10, 10, 11, 11, 11, 10, 9, 11, 10, 12, 11, 12, 11, 10, 9, 8, 7, 9, 10, 11, 11, 13, 12, 12, 11, 12, 12, 12, 12, 11, 10, 9, 8, 7
Offset: 1
Keywords
Examples
Let m = -1. Then, n = 1..9 can be expressed using a(n) m's as follows: a(1)=2: 1 = (-1)*(-1) = m*m. a(2)=3: 2 = (-2)*(-1) = (m+m)*m. a(3)=4: 3 = (-3)*(-1) = (m+m+m)*m. a(4)=4: 4 = (-2)*(-2) = (m+m)*(m+m). a(5)=6: 5 = (-5)*(-1) = (m+m+m+m+m)*m. a(6)=5: 6 = (-2)*(-3) = (m+m)*(m+m+m). a(7)=7: 7 = 8 +(-1) = (m+m+m+m)*(m+m)+m. a(8)=6: 8 = (-4)*(-2) = (m+m+m+m)*(m+m). a(9)=6: 9 = (-3)^ 2 = (m+m+m)^((m+m)*m).
Links
- Edgar Deshayes, Java program
Crossrefs
Cf. A025280 (same with +1).
Programs
-
Java
// see linked program
Comments