cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A342298 a(n) is the greatest k such that A342263(k) = n.

Original entry on oeis.org

2, 25, 931, 504455, 67539587599, 585462196329239562271, 21690980800898420269408456526391711768639, 14792097944732868603877386771665610972834204784426907551800717772696470224928895
Offset: 0

Views

Author

Rémy Sigrist, Mar 07 2021

Keywords

Links

Crossrefs

Cf. A052944, A070939, A247241, A342263.

Programs

  • PARI
    See Links section.

Formula

A070939(a(n)) = A052944(n+1).

A354614 Number of distinct substrings of length A342263(n) that appear at least twice in the binary expansion of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 1
Offset: 0

Views

Author

Peter Kagey, Jul 08 2022

Keywords

Comments

Records occur at indices 0, 9, 69, 279, 8501, 17003, 49771, 136030, ...

Examples

			The binary expansion of 8501 is 10000100110101. And there are a(8501) = 5 longest repeated substrings: 101, 100, 010, 001, and 000, as illustrated below.
  10000100110101
  .........101..
  ...........101
  100...........
  .....100......
  ....010.......
  ..........010.
  ...001........
  ......001.....
  .000..........
  ..000.........

Crossrefs

Cf. A342263.

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

Original entry on oeis.org

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

Views

Author

Peter Kagey, Jul 08 2022

Keywords

Comments

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

Examples

			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.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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