A361755 Irregular triangle T(n, k), n >= 0, k = 1..2^A007895(n), read by rows; the n-th row lists the numbers k such that the Fibonacci numbers that appear in the Zeckendorf representation of k also appear in that of n.

0, 0, 1, 0, 2, 0, 3, 0, 1, 3, 4, 0, 5, 0, 1, 5, 6, 0, 2, 5, 7, 0, 8, 0, 1, 8, 9, 0, 2, 8, 10, 0, 3, 8, 11, 0, 1, 3, 4, 8, 9, 11, 12, 0, 13, 0, 1, 13, 14, 0, 2, 13, 15, 0, 3, 13, 16, 0, 1, 3, 4, 13, 14, 16, 17, 0, 5, 13, 18, 0, 1, 5, 6, 13, 14, 18, 19, 0, 2, 5, 7, 13, 15, 18, 20

Offset: 0

Author

Rémy Sigrist, Mar 23 2023

Keywords

• nonn
• tabf
• base

Comments

In other words, the n-th row lists the numbers k such that A003714(n) AND A003714(k) = A003714(k) (where AND denotes the bitwise AND operator).

The Zeckendorf representation is also known as the greedy Fibonacci representation (see A356771 for further details).

Examples

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

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10924 (rows for n = 0..610 flattened)
• Rémy Sigrist, PARI program
• Index entries for sequences related to Zeckendorf expansion of n

Crossrefs

See A361756 for a similar sequence.

Cf. A003714, A007895, A139764, A295989, A356771.

Programs

PARI

See Links section.

Formula

T(n, 1) = 0.

T(n, 2) = A139764(n) for any n > 0.

T(n, 2^A007895(n)) = n.