A330925 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*y.

0, 0, 0, 1, 0, 2, 2, 3, 0, 4, 4, 6, 4, 6, 6, 9, 0, 8, 8, 12, 8, 12, 12, 15, 8, 12, 12, 18, 12, 18, 18, 21, 0, 16, 16, 24, 16, 24, 24, 28, 16, 24, 24, 30, 24, 30, 30, 35, 16, 24, 24, 36, 24, 36, 36, 42, 24, 36, 36, 42, 36, 42, 42, 49, 0, 32, 32, 48, 32, 48, 48

Offset

0,6

Comments

Interleaving (or shuffling) two strings means combining all their characters while preserving the order of all characters in individual strings; for example, "12345" is the interleaving of "14" and "235".

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Rémy Sigrist, C program for A330925

Index entries for sequences related to binary expansion of n

Formula

a(n) = 0 iff n is zero or a power of 2.

a(2*n) = 2*a(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*y
  -------  -  -  ---
  "101"    5  0    0
  "1/01"   1  1    1
  "10/1"   2  1    2
  "1/0/1"  3  0    0
- hence a(5) = 2.

Prog

(C) See Links section.

Crossrefs

Cf. A330955 (x AND y variant), A330958 (x OR y variant), A330959 (x XOR y variant).

Cf. A330956 (min(x, y) variant), A330957 (max(x, y) variant).

Cf. A330960 (x + y variant), A330961 (x - y variant).

Cf. A330962 (x^2 + y^2 variant), A330963 (x^2 - y^2 variant).

See A327186 for similar sequences where we split the binary representation.

Sequence in context: A079626 A257697 A088864 * A191361 A199784 A349384

Adjacent sequences: A330922 A330923 A330924 * A330926 A330927 A330928

Keyword

nonn,base

Author

Rémy Sigrist, Jan 03 2020

Status

approved