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A341054
For any number n with balanced ternary expansion (d_1, ..., d_k), the balanced ternary expansion of a(n), say (t_1, ..., t_k), satisfies t_m = d_1 + ... + d_m mod 3 for m = 1..k.
2
0, 1, 3, 4, 2, 8, 9, 10, 12, 13, 11, 7, 5, 6, 25, 23, 24, 26, 27, 28, 30, 31, 29, 35, 36, 37, 39, 40, 38, 34, 32, 33, 21, 22, 20, 16, 14, 15, 17, 18, 19, 75, 76, 74, 70, 68, 69, 71, 72, 73, 79, 77, 78, 80, 81, 82, 84, 85, 83, 89, 90, 91, 93, 94, 92, 88, 86, 87
OFFSET
0,3
COMMENTS
This sequence is similar to A006068.
This sequence is a permutation of the nonnegative integers with inverse A341055.
EXAMPLE
The first terms, alongside their balanced ternary expansion (with T's standing for -1's), are:
n a(n) bter(n) bter(a(n))
-- ---- ------- ----------
0 0 0 0
1 1 1 1
2 3 1T 10
3 4 10 11
4 2 11 1T
5 8 1TT 10T
6 9 1T0 100
7 10 1T1 101
8 12 10T 110
9 13 100 111
10 11 101 11T
11 7 11T 1T1
12 5 110 1TT
13 6 111 1T0
14 25 1TTT 10T1
15 23 1TT0 10TT
16 24 1TT1 10T0
PROG
(PARI) a(n) = { my (d=[], s=Mod(0, 3)); while (n, my (t=centerlift(Mod(n, 3))); n=(n-t)\3; d=concat(t, d)); for (k=1, #d, d[k] = centerlift(s+=d[k])); fromdigits(d, 3) }
CROSSREFS
Cf. A006068, A059095, A341055 (inverse).
Sequence in context: A143053 A220508 A316323 * A120239 A082362 A082364
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 25 2021
STATUS
approved