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

1,1

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]

Links

Table of n, a(n) for n=1..65.

Formula

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

Example

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

Crossrefs

Sequence in context: A268221 A086176 A015789 * A135280 A100436 A348011

Adjacent sequences: A145018 A145019 A145020 * A145022 A145023 A145024

Keyword

easy,nonn

Author

Ken Levasseur, Sep 29 2008

Status

approved