A365214 Least k such that the binary representation of 3^k has exactly n 1's, or -1 if no such k exists.

0, 1, 4, 3, 7, 5, -1, 9, 10, 12, 13, -1, 11, 14, 15, 24, 19, 25, 22, 21, -1, 23

Offset: 1

Author

Pontus von Brömssen, Aug 26 2023

Keywords

• sign
• base
• more

Comments

Least k such that A011754(k) = n, or -1 if no such k exists.

The first 22 terms are from Dimitrov and Howe (2021). After a(22), the sequence continues (with the -1's conjectural but very likely correct) -1, 26, 28, 31, 36, 40, 34, 27, -1, 35, 49, 33, 53, 38, -1, 42, 41, 57, 48, 52, -1, -1, 46, 51, 67, 59, 62, -1, ... .

Links

• Vassil S. Dimitrov and Everett W. Howe, Powers of 3 with few nonzero bits and a conjecture of Erdős, arXiv:2105.06440 [math.NT], 2021.

Crossrefs

Cf. A011754, A364650, A365215, A375472.