A274601 a(n) = 2*3^(s-1) - n, where s is the number of trits of n in balanced ternary form.

1, 4, 3, 2, 13, 12, 11, 10, 9, 8, 7, 6, 5, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100

Offset: 1

Author

Lei Zhou, Nov 10 2016

Keywords

• nonn
• base
• easy

Comments

Analogous to a bit, a ternary digit is a trit.

Per the definition, n + a(n) = 2*3^(s-1), where s is the number of trits of n and a(n), n and a(n) form a decomposition of 2*3^(s-1).

Examples

			For n=1 the balanced ternary form of 1 is 1, which has 1 trits. 2*3^(1-1)-1 = 1, so a(1) = 1.
For n=2 the balanced ternary form of 2 is 1T, which has 2 trits. 2*3^(2-1)-2 = 4, so a(2) = 4.
For n=3 the balanced ternary form of 3 is 10, which has 2 trits. 2*3^(2-1)-3 = 3, so a(2) = 3.
...
For n=62 the balanced ternary form of 62 is 1T10T, which has 5 trits. 2*3^(5-1)-62 = 100, so a(62) = 100.
		

Links

• Lei Zhou, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A117966, A134021, A140267, A134028.

Programs

Mathematica

Table[2*3^(Floor[Log[3, 2*n - 1]]) - n, {n, 1, 62}]

PARI

a(n) = 2*3^logint(2*n-1,3)-n \\ Jason Yuen, Nov 18 2024

Python

from sympy import integer_log
def a(n): return 2*3**(integer_log(2*n - 1, 3)[0]) - n
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 10 2017

Formula

a(n) = 2*3^(floor(log_3(2*n-1))) - n. [corrected by Jason Yuen, Nov 18 2024]