A362755 Irregular triangle read by rows; the n-th row lists the numbers k such that if phi^e appears in the base phi expansion of k then phi^e also appears in the base phi expansion of n (where phi denotes A001622, the golden ratio).

0, 0, 1, 0, 2, 0, 3, 0, 1, 3, 4, 0, 5, 0, 6, 0, 7, 0, 1, 7, 8, 0, 2, 7, 9, 0, 3, 7, 10, 0, 1, 3, 4, 7, 8, 10, 11, 0, 12, 0, 13, 0, 14, 0, 1, 14, 15, 0, 16, 0, 17, 0, 18, 0, 1, 18, 19, 0, 2, 18, 20, 0, 3, 18, 21, 0, 1, 3, 4, 18, 19, 21, 22, 0, 5, 18, 23, 0, 6, 18, 24

Offset: 0

Author

Rémy Sigrist, May 02 2023

Keywords

• nonn
• base
• tabf

Comments

See A361755 for a similar sequence.

Examples

			Triangle 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, 6
   7  0, 7
   8  0, 1, 7, 8
   9  0, 2, 7, 9
  10  0, 3, 7, 10
  11  0, 1, 3, 4, 7, 8, 10, 11
  12  0, 12
  13  0, 13
  14  0, 14
  15  0, 1, 14, 15
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..9999 (rows for n = 0..1060 flattened)
• Rémy Sigrist, PARI program
• Wikipedia, Golden ratio base

Crossrefs

Cf. A001622, A104605, A214971, A361755.

Programs

PARI

See Links section.

Formula

T(n, 1) = 0.

T(n, 2) = 1 iff n belongs to A214971.