A330963 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 abs(x^2 - y^2).

0, 1, 1, 0, 1, 0, 3, 8, 1, 0, 0, 5, 0, 5, 5, 0, 1, 0, 0, 5, 0, 5, 5, 0, 9, 7, 5, 0, 7, 16, 27, 40, 1, 0, 0, 5, 0, 5, 5, 0, 0, 7, 5, 0, 7, 0, 11, 24, 0, 8, 5, 0, 7, 0, 0, 13, 20, 11, 0, 13, 0, 13, 13, 0, 1, 0, 0, 5, 0, 5, 5, 0, 0, 7, 5, 0, 7, 0, 11, 24, 0, 8, 5

Offset

0,7

Links

Table of n, a(n) for n=0..82.

Rémy Sigrist, C program for A330963

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^2-y^2|
  -------  -  -  ---------
  "101"    5  0         25
  "1/01"   1  1          0
  "10/1"   2  1          3
  "1/0/1"  3  0          9
- hence a(5) = 0.

Prog

(C) See Links section.

Crossrefs

See A330925 for similar sequences.

Cf. A327195.

Sequence in context: A076482 A225802 A156827 * A327195 A140272 A210962

Adjacent sequences: A330960 A330961 A330962 * A330964 A330965 A330966

Keyword

nonn,base

Author

Rémy Sigrist, Jan 04 2020

Status

approved