A331579 Position of first appearance of n in A124758 (products of compositions in standard order).

1, 2, 4, 8, 16, 18, 64, 34, 36, 66, 1024, 68, 4096, 258, 132, 136, 65536, 146, 262144, 264, 516, 4098

Offset: 1

Author

Gus Wiseman, Mar 20 2020

Keywords

• nonn
• more

Comments

A composition of n is a finite sequence of positive integers summing to n. 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 list of terms together with the corresponding compositions begins:
       1: (1)
       2: (2)
       4: (3)
       8: (4)
      16: (5)
      18: (3,2)
      64: (7)
      34: (4,2)
      36: (3,3)
      66: (5,2)
    1024: (11)
      68: (4,3)
    4096: (13)
     258: (7,2)
     132: (5,3)
     136: (4,4)
   65536: (17)
     146: (3,3,2)
  262144: (19)
     264: (5,4)
		

Crossrefs

The product of prime indices is A003963.

The sum of binary indices is A029931.

The sum of prime indices is A056239.

Sums of compositions in standard order are A070939.

The product of binary indices is A096111.

All terms belong to A114994.

Products of compositions in standard order are A124758.

Cf. A000120, A048793, A066099, A164894, A233249, A233564, A272919, A326674, A333217, A333219, A333220, A333223.

Programs

Mathematica

stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
q=Table[Times@@stc[n],{n,1000}];
Table[Position[q,i][[1,1]],{i,First[Split[Union[q],#1+1==#2&]]}]