A354616 Numbers such that every bit in its binary expansion is in a substring of length A342263(n) that appears more than once.

3, 7, 9, 10, 12, 15, 19, 21, 25, 31, 34, 36, 37, 40, 41, 42, 45, 46, 54, 56, 58, 63, 69, 73, 77, 81, 85, 89, 91, 99, 109, 127, 132, 136, 137, 141, 142, 144, 145, 146, 148, 150, 151, 153, 154, 157, 165, 166, 167, 170, 173, 175, 177, 178, 181, 182, 184, 185, 187

Offset

1,1

Comments

This list contains all terms of the form 2^n - 1 for n >= 2.

Links

Table of n, a(n) for n=1..59.

Example

The binary expansion of 8501 is 10000100110101, and there are A354614(8501) = 5 repeated substrings of length A342263(8501) = 3: 101, 100, 010, 001, and 000. Every bit in the binary expansion of 8501 appears in one or more of these substrings, so 8501 is in the list.
  10000100110101
  .........101..
  ...........101
  100...........
  .....100......
  ....010.......
  ..........010.
  ...001........
  ......001.....
  .000..........
  ..000.........

Crossrefs

Cf. A342263, A354614.

Sequence in context: A081339 A063551 A160800 * A099248 A082575 A284526

Adjacent sequences: A354613 A354614 A354615 * A354617 A354618 A354619

Keyword

base,nonn

Author

Peter Kagey, Jul 08 2022

Status

approved