

A274601


a(n) = 2*3^(s1)  n, where s is the number of trits of n in balanced ternary form.


2



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
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OFFSET

1,2


COMMENTS

Analogous to a bit, a ternary digit is a trit (trinary digit).
Per the definition, n + a(n) = 2*3^(s1), where s is the number of trits of n and a(n), n and a(n) form a decomposition of 2*3^(s1).


LINKS



FORMULA

a(n) = 2*3^(floor(log(2*n1)/log(3)).


EXAMPLE

For n=1 the balanced ternary form of 1 is 1, which has 1 trits. 2*3^(11)1 = 1, so a(1) = 1.
For n=2 the balanced ternary form of 2 is 1T, which has 2 trits. 2*3^(21)2 = 4, so a(2) = 4.
For n=3 the balanced ternary form of 3 is 10, which has 2 trits. 2*3^(21)3 = 3, so a(2) = 3.
...
For n=62 the balanced ternary form of 62 is 1T10T, which has 5 trits. 2^(3^(51)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 log, floor
def a(n): return 2*3**(floor(log(2*n  1, 3)))  n


CROSSREFS



KEYWORD

nonn,base,easy


AUTHOR



STATUS

approved



