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A353826
The positions of nonzero digits in the ternary expansions of n and a(n) are the same, and the k-th rightmost nonzero digit in a(n) equals modulo 3 the product of the k rightmost nonzero digits in n.
5
0, 1, 2, 3, 4, 8, 6, 7, 5, 9, 10, 20, 12, 13, 26, 24, 25, 14, 18, 19, 11, 21, 22, 17, 15, 16, 23, 27, 28, 56, 30, 31, 62, 60, 61, 32, 36, 37, 74, 39, 40, 80, 78, 79, 41, 72, 73, 38, 75, 76, 44, 42, 43, 77, 54, 55, 29, 57, 58, 35, 33, 34, 59, 63, 64, 47, 66, 67
OFFSET
0,3
COMMENTS
This sequence is a permutation of the nonnegative integers with inverse A353827.
A number is a fixed point of this sequence iff it has at most one digit 2 in its ternary expansion, that digit 2 being its leftmost nonzero digit.
FORMULA
a(3*n) = 3*a(n).
a(3*n + 1) = 3*a(n) + 1.
EXAMPLE
The first terms, in decimal and in ternary, are:
n a(n) ter(n) ter(a(n))
-- ---- ------ ---------
0 0 0 0
1 1 1 1
2 2 2 2
3 3 10 10
4 4 11 11
5 8 12 22
6 6 20 20
7 7 21 21
8 5 22 12
9 9 100 100
10 10 101 101
11 20 102 202
12 12 110 110
PROG
(PARI) a(n) = { my (d=digits(n, 3), p=1); forstep (k=#d, 1, -1, if (d[k], d[k]=p*=d[k])); fromdigits(d%3, 3) }
CROSSREFS
See A305458, A353824, A353828, A353830 for similar sequences.
Cf. A353827 (inverse).
Sequence in context: A222247 A338242 A353827 * A123492 A123493 A123715
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 08 2022
STATUS
approved