A382176 Numbers k such that the period of 1/k when expanded in golden ratio base is palindromic.

1, 2, 36, 38, 644, 646, 682, 11556, 11558, 11592, 12198, 12238

Offset: 1

Author

Amiram Eldar, Mar 17 2025

Keywords

• nonn
• base
• more

Comments

a(13) > 80000, if it exists.

Examples

			  n | a(n) | period (row n of A382172)
  --+------+-----------------------------------------------------------------------
  1 |    1 | 0
  2 |    2 | 0, 1, 0
  3 |   36 | 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
  4 |   38 | 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
		

Crossrefs

Cf. A330722, A362781, A373085, A382172, A382173, A382174, A382175.

Programs

Mathematica

q[k_] := PalindromeQ[RealDigits[1/k, GoldenRatio, A001175[k], -1][[1]]]; Select[Range[1000], q] (* using A001175[n] from A001175 *)