A333492 Position of first appearance of n in A271410 (LCM of binary indices).

1, 2, 4, 8, 16, 6, 64, 128, 256, 18, 1024, 12, 4096, 66, 20, 32768, 65536, 258, 262144, 24, 68, 1026, 4194304, 132, 16777216, 4098, 67108864, 72, 268435456, 22, 1073741824, 2147483648, 1028, 65538, 80, 264, 68719476736, 262146, 4100, 144, 1099511627776, 70, 4398046511104

Offset

1,2

Comments

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

Links

Giovanni Resta, Table of n, a(n) for n = 1..1000

Example

The sequence together with the corresponding binary expansions and binary indices begins:
      1:                 1 ~ {1}
      2:                10 ~ {2}
      4:               100 ~ {3}
      8:              1000 ~ {4}
     16:             10000 ~ {5}
      6:               110 ~ {2,3}
     64:           1000000 ~ {7}
    128:          10000000 ~ {8}
    256:         100000000 ~ {9}
     18:             10010 ~ {2,5}
   1024:       10000000000 ~ {11}
     12:              1100 ~ {3,4}
   4096:     1000000000000 ~ {13}
     66:           1000010 ~ {2,7}
     20:             10100 ~ {3,5}
  32768:  1000000000000000 ~ {16}
  65536: 10000000000000000 ~ {17}
    258:         100000010 ~ {2,9}

Mathematica

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

Crossrefs

The version for prime indices is A330225.

The version for standard compositions is A333225.

Let q(k) be the binary indices of k:

- The sum of q(k) is A029931(k).

- The elements of q(k) are row k of A048793.

- The product of q(k) is A096111(k).

- The LCM of q(k) is A271410(k).

- The GCD of q(k) is A326674(k).

GCD of prime indices is A289508.

LCM of prime indices is A290103.

LCM of standard compositions is A333226.

Cf. A000120, A066099, A070939, A074761, A076078, A124767, A285572, A324837, A328219, A328451, A331579, A333227.

Sequence in context: A167425 A212638 A016018 * A228845 A228846 A070336

Adjacent sequences: A333489 A333490 A333491 * A333493 A333494 A333495

Keyword

nonn

Author

Gus Wiseman, Mar 28 2020

Extensions

Terms a(23) and beyond from Giovanni Resta, Mar 29 2020

Status

approved