A330960 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 least possible value of x + y.

0, 1, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 3, 4, 5, 6, 1, 2, 3, 4, 3, 4, 5, 6, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 3, 4, 5, 6, 3, 4, 5, 6, 7, 8, 9, 10, 3, 4, 5, 6, 7, 8, 9, 10, 7, 8, 9, 10, 11, 12, 13, 14, 1, 2, 3, 4, 3, 4, 5, 6, 3, 4, 5, 6, 7, 8, 9, 10, 3, 4, 5, 6

Offset: 0

Author

Rémy Sigrist, Jan 04 2020

Keywords

• nonn
• base

Examples

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

Links

• Rémy Sigrist, C program for A330960
• Index entries for sequences related to binary expansion of n

Crossrefs

See A330925 for similar sequences.

Cf. A327189.

Programs

C

See Links section.