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

1,2

Comments

Analogous to a bit, a ternary digit is a trit (trinary digit).

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).

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A117966, A134021, A140267, A134028.

Sequence in context: A182142 A033881 A099406 * A202696 A319541 A239020

Adjacent sequences: A274598 A274599 A274600 * A274602 A274603 A274604

Keyword

nonn,base,easy

Author

Lei Zhou, Nov 10 2016

Status

approved