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

0,5

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).

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

Formula

T(n, 1) = 0.

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

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

See A361756 for a similar sequence.

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

Sequence in context: A362110 A236138 A363930 * A362755 A035614 A212138

Adjacent sequences: A361752 A361753 A361754 * A361756 A361757 A361758

Keyword

nonn,tabf,base

Author

Rémy Sigrist, Mar 23 2023

Status

approved