A382176 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

a(13) > 80000, if it exists.

LINKS

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

KEYWORD

nonn,base,more

AUTHOR

Amiram Eldar, Mar 17 2025

STATUS

approved