A363930 Irregular table T(n, k), n >= 0, k = 1..A363710(n), read by rows; the n-th row lists the nonnegative numbers m <= n such that A003188(m) AND A003188(n-m) = 0 (where AND denotes the bitwise AND operator).

0, 0, 1, 0, 2, 0, 3, 0, 1, 3, 4, 0, 1, 4, 5, 0, 6, 0, 7, 0, 1, 7, 8, 0, 1, 2, 3, 6, 7, 8, 9, 0, 2, 3, 7, 8, 10, 0, 3, 8, 11, 0, 1, 3, 9, 11, 12, 0, 1, 12, 13, 0, 14, 0, 15, 0, 1, 15, 16, 0, 1, 2, 3, 14, 15, 16, 17, 0, 2, 3, 4, 6, 12, 14, 15, 16, 18, 0, 3, 4, 7, 12, 15, 16, 19

Offset

0,5

Comments

This sequence is related to the T-square fractal (see A363710).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..13126 (rows for n = 0..2^9 flattened)

Wikipedia, T-square (fractal)

Formula

T(n, 1) = 0.

T(n, A363710(n)) = n.

T(n, k) + T(n, A363710(n)+1-k) = n.

Example

Table T(n, k) begins:
  n   n-th row
  --  ----------------------
   0  0
   1  0, 1
   2  0, 2
   3  0, 3
   4  0, 1, 3, 4
   5  0, 1, 4, 5
   6  0, 6
   7  0, 7
   8  0, 1, 7, 8
   9  0, 1, 2, 3, 6, 7, 8, 9
  10  0, 2, 3, 7, 8, 10
  11  0, 3, 8, 11
  12  0, 1, 3, 9, 11, 12
  13  0, 1, 12, 13
  14  0, 14
  15  0, 15
  16  0, 1, 15, 16

Prog

(PARI) row(n) = { select (m -> bitand(bitxor(m, m\2), bitxor(n-m, (n-m)\2))==0, [0..n]) }

Crossrefs

See A295989, A353174 and A362327 for similar sequences.

Cf. A003188, A363710.

Sequence in context: A336316 A362110 A236138 * A361755 A362755 A035614

Adjacent sequences: A363927 A363928 A363929 * A363931 A363932 A363933

Keyword

nonn,base,tabf

Author

Rémy Sigrist, Jun 28 2023

Status

approved