A333225 Position of first appearance of n in A333226 (LCMs of compositions in standard order).

1, 2, 4, 8, 16, 18, 64, 128, 256, 66, 1024, 68, 4096, 258, 132, 32768, 65536, 1026, 262144, 264, 516, 4098

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..22.

Example

The sequence together with the corresponding compositions begins:
       1: (1)
       2: (2)
       4: (3)
       8: (4)
      16: (5)
      18: (3,2)
      64: (7)
     128: (8)
     256: (9)
      66: (5,2)
    1024: (11)
      68: (4,3)
    4096: (13)
     258: (7,2)
     132: (5,3)
   32768: (16)
   65536: (17)
    1026: (9,2)
  262144: (19)
     264: (5,4)

Mathematica

stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
q=Table[LCM@@stc[n], {n, 10000}];
Table[Position[q, i][[1, 1]], {i, First[Split[Union[q], #1+1==#2&]]}]

Crossrefs

The version for binary indices is A333492.

The version for prime indices is A330225.

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, A074971, A076078, A233564, A271410, A289508, A289509, A290103, A333227.

Sequence in context: A133809 A128700 A331579 * A212204 A184986 A018547

Adjacent sequences: A333222 A333223 A333224 * A333226 A333227 A333228

Keyword

nonn,more

Author

Gus Wiseman, Mar 26 2020

Status

approved