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

1,2

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.

Links

Table of n, a(n) for n=1..86.

Mathematica

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

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.

Sequence in context: A284267 A296525 A333766 * A175548 A038571 A008687

Adjacent sequences: A333223 A333224 A333225 * A333227 A333228 A333229

Keyword

nonn

Author

Gus Wiseman, Mar 26 2020

Status

approved