A333226 Least common multiple of the n-th composition in standard order.

1, 2, 1, 3, 2, 2, 1, 4, 3, 2, 2, 3, 2, 2, 1, 5, 4, 6, 3, 6, 2, 2, 2, 4, 3, 2, 2, 3, 2, 2, 1, 6, 5, 4, 4, 3, 6, 6, 3, 4, 6, 2, 2, 6, 2, 2, 2, 5, 4, 6, 3, 6, 2, 2, 2, 4, 3, 2, 2, 3, 2, 2, 1, 7, 6, 10, 5, 12, 4, 4, 4, 12, 3, 6, 6, 3, 6, 6, 3, 10, 4, 6, 6, 6, 2, 2

Offset: 1

Author

Gus Wiseman, Mar 26 2020

Keywords

• nonn

Comments

The k-th composition in standard order (row k of A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again.

Crossrefs

The version for binary indices is A271410.

The version for prime indices is A290103.

Positions of first appearances are A333225.

Let q(k) be the k-th composition in standard order:

- The terms of q(k) are row k of A066099.

- The sum of q(k) is A070939(k).

- The product of q(k) is A124758(k).

- The GCD of q(k) is A326674(k).

- The LCM of q(k) is A333226(k).

Cf. A000120, A029931, A048793, A074971, A076078, A233564, A285572, A289508, A289509, A324837, A333227, A333492.

Programs

Mathematica

stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
Table[LCM@@stc[n],{n,100}]