A382173 a(n) is the sum of row n of A382172.

0, 1, 2, 1, 6, 7, 4, 2, 6, 16, 1, 5, 8, 14, 10, 5, 10, 6, 3, 15, 2, 7, 13, 4, 26, 24, 19, 9, 1, 31, 6, 10, 8, 10, 20, 4, 22, 2, 13, 14, 11, 11, 24, 5, 31, 13, 8, 4, 30, 80, 17, 20, 30, 18, 2, 11, 17, 9, 14, 30, 16, 5, 10, 25, 36, 29, 38, 6, 9, 63, 16, 2, 40, 64

Offset: 1

Author

Amiram Eldar, Mar 17 2025

Keywords

• nonn
• easy
• base

Comments

The sum of digits (or, equivalently, the number of 1's) of the period of 1/n when expanded in golden ratio base.

Examples

			The first 5 terms and the corresponding rows of A382172 are:
  n | a(n) | row n
 ---+------+-----------------------------------------------------------
  1 |    0 | 0
  2 |    1 | 0, 1, 0
  3 |    2 | 0, 0, 1, 0, 1, 0, 0, 0
  4 |    1 | 0, 0, 1, 0, 0, 0
  5 |    6 | 0, 0, 0 ,1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000032, A002878, A007733, A055778, A093960, A276350, A382172, A382174, A382175, A382176.

Programs

Mathematica

a[n_] := Total[RealDigits[1/n, GoldenRatio, A001175[n], -1][[1]]]; Array[a, 100] (* using A001175[n] from A001175 *)