A330955 For any n >= 0: consider all pairs of numbers (x, y) whose binary representations can be interleaved (or shuffled) to produce the binary representation of n (possibly with leading zeros); a(n) is the greatest possible value of x AND y (where AND denotes the bitwise AND operator).

0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 2, 2, 2, 2, 2, 3, 0, 1, 2, 2, 2, 2, 2, 3, 0, 1, 2, 3, 2, 2, 2, 3, 0, 1, 2, 2, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 4, 5, 4, 4, 4, 5, 4, 5, 6, 6, 4, 4, 6, 6, 6, 6, 6, 7, 0, 1, 2, 2, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 4, 5, 4, 4, 4, 5, 4, 5, 6

Offset

0,11

Links

Table of n, a(n) for n=0..86.

Rémy Sigrist, C program for A330955

Index entries for sequences related to binary expansion of n

Example

For n = 5:
- the binary representation of 5 is "101",
- the possible values for (x, y), restricted to x >= y without loss of generality, are:
  bin(5)   x  y  x AND y
  -------  -  -  -------
  "101"    5  0        0
  "1/01"   1  1        1
  "10/1"   2  1        0
  "1/0/1"  3  0        0
- hence a(5) = 1.

Prog

(C) See Links section.

Crossrefs

See A330925 for similar sequences.

Cf. A327188.

Sequence in context: A319991 A323275 A139514 * A330956 A190617 A068323

Adjacent sequences: A330952 A330953 A330954 * A330956 A330957 A330958

Keyword

nonn,base

Author

Rémy Sigrist, Jan 04 2020

Status

approved