A352773 -id:A352773 - cp's OEIS frontend

A352772 a(n) = A109812(n) AND A109812(n+2) (where AND denotes the bitwise AND operator).

0, 2, 0, 1, 8, 0, 2, 0, 2, 8, 16, 12, 0, 6, 0, 1, 16, 1, 4, 3, 32, 17, 32, 5, 32, 13, 0, 6, 0, 2, 9, 2, 1, 2, 1, 8, 5, 64, 19, 64, 3, 4, 3, 12, 64, 36, 80, 0, 24, 0, 1, 2, 1, 2, 33, 2, 4, 2, 4, 34, 65, 48, 72, 48, 66, 48, 70, 8, 3, 8, 3, 12, 128, 28, 128, 11

Offset: 1

Rémy Sigrist, Apr 02 2022

The binary expansions of two consecutive terms of A109812 have no common 1's, but the binary expansions of two terms at distance 2 can have some common 1's; this sequence gives these common 1's.

			For n = 42:
- A109812(42) = 68,
- A109812(44) = 28,
- so a(42) = 68 AND 28 = 4.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Log-log scatterplot of the first 2^20 terms
Rémy Sigrist, C++ program

Cf. A109812, A352773.

A352998 a(n) is the least k > 0 such that the binary expansions of A109812(n) and A109812(n + 2*k) have no common 1-bit.

Original entry on oeis.org

1, 2, 1, 2, 2, 1, 3, 1, 2, 10, 2, 3, 1, 2, 1, 11, 2, 6, 2, 10, 4, 8, 3, 4, 2, 3, 1, 6, 1, 4, 8, 6, 13, 2, 12, 2, 5, 5, 18, 2, 9, 4, 2, 3, 7, 2, 3, 1, 2, 1, 12, 9, 6, 15, 2, 4, 9, 6, 2, 12, 8, 4, 7, 3, 6, 2, 5, 8, 4, 8, 2, 17, 4, 5, 4, 16, 2, 19, 3, 14, 5, 7

Offset: 1

Rémy Sigrist, Apr 14 2022

			For n = 18:
- we have:
      k  A109812(18+2*k)  A109812(18) AND A109812(18+2*k)
      -  ---------------  -------------------------------
      0               33                               33
      1               11                                1
      2               19                                1
      3               21                                1
      4               13                                1
      5               15                                1
      6               22                                0
- so a(18) = 6.

Rémy Sigrist, Scatterplot of the first million terms
Rémy Sigrist, C++ program

Cf. A109812, A352773 (positions of 1's), A352999.

a(n) >= A352999(n).

cp's OEIS Frontend

A352772 a(n) = A109812(n) AND A109812(n+2) (where AND denotes the bitwise AND operator).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs