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

Author

Gus Wiseman, Mar 26 2020

Keywords

• nonn
• more

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.

Examples

			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)
		

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.

Programs

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&]]}]