A145021 a(n) = number of different positive integers that can be formed from different groupings of expressions of the form n op1 n op2 n op3 n, where each of op1, op2 and op3 are addition, subtraction, multiplication or division.

4, 10, 20, 25, 27, 29, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30

Offset: 1

Author

Ken Levasseur, Sep 29 2008

Keywords

• easy
• nonn

Comments

If one uses all 4^3=64 forms of this type but no parentheses, the sequence starts 4,9,15,13,15,14... In this case 4/4/4/4=1/4/4=1/16 is not an integer (association left-to-right), whereas with parenthesis one could write (4/4)/(4/4)=1, an integer, for example. The definition need clarification in this respect. [From R. J. Mathar, Jan 22 2009]

Examples

			You can form the numbers 1, 2, 3, 4 with 4 ones; hence the first term is 4.
		

Formula

If k >3, a(2k-1)=30 and a(2k)=31. - Ken Levasseur, Oct 01 2008