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

1,2

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.

Links

Table of n, a(n) for n=1..22.

Example

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)

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&]]}]

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.

Sequence in context: A364061 A133809 A128700 * A333225 A212204 A184986

Adjacent sequences: A331576 A331577 A331578 * A331580 A331581 A331582

Keyword

nonn,more

Author

Gus Wiseman, Mar 20 2020

Status

approved