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

0,5

Comments

See A361755 for a similar sequence.

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

Formula

T(n, 1) = 0.

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A001622, A104605, A214971, A361755.

Sequence in context: A236138 A363930 A361755 * A035614 A212138 A133735

Adjacent sequences: A362752 A362753 A362754 * A362756 A362757 A362758

Keyword

nonn,base,tabf

Author

Rémy Sigrist, May 02 2023

Status

approved