A328732 Irregular table read by rows; for any n >= 0, the n-th row contains the numbers of the form u - v with u + v = n and u AND v = 0 (where AND denotes the bitwise AND operator), in ascending order.

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

Offset: 0

Author

Rémy Sigrist, Oct 26 2019

Keywords

• sign
• base
• tabf

Comments

The n-th row:

- has A001316(n) terms,

- has -n as first term and n as last term,

- has least positive term T(n, A001316(n)/2+1) = A080079(n) (when n > 0).

Examples

			Table begins:
    0;
   -1,   1;
   -2,   2;
   -3,  -1,   1,   3;
   -4,   4;
   -5,  -3,   3,   5;
   -6,  -2,   2,   6;
   -7,  -5,  -3,  -1,   1,   3,   5,   7;
   -8,   8;
   -9,  -7,   7,   9;
  -10,  -6,   6,  10;
  -11,  -9,  -7,  -5,   5,   7,   9,  11;
  -12,  -4,   4,  12;
  -13, -11,  -5,  -3,   3,   5,  11,  13;
  ...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6562 (Rows for n = 0..256)
• Rémy Sigrist, Scatterplot of (n, T(n, k)) for n = 0..1024 and k = 1..A001316(n)

Crossrefs

Cf. A001316, A080079.

Programs

PARI

row(n) = my (r=[0], b=Vecrev(binary(n))); for (k=0, #b-1, if (b[k+1], r=concat(apply(v -> [v-2^k,v+2^k], r)))); Set(r)