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A353824
The positions of nonzero digits in the ternary expansions of n and a(n) are the same, and the k-th leftmost nonzero digit in a(n) equals modulo 3 the product of the k leftmost nonzero digits in n.
5
0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 12, 13, 14, 15, 17, 16, 18, 20, 19, 24, 26, 25, 21, 22, 23, 27, 28, 29, 30, 31, 32, 33, 35, 34, 36, 37, 38, 39, 40, 41, 42, 44, 43, 45, 47, 46, 51, 53, 52, 48, 49, 50, 54, 56, 55, 60, 62, 61, 57, 58, 59, 72, 74, 73, 78, 80
OFFSET
0,3
COMMENTS
This sequence is a permutation of the nonnegative integers with inverse A353825.
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 rightmost nonzero digit.
FORMULA
a(3*n) = 3*a(n).
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 5 12 12
6 6 20 20
7 8 21 22
8 7 22 21
9 9 100 100
10 10 101 101
11 11 102 102
12 12 110 110
PROG
(PARI) a(n) = { my (d=digits(n, 3), p=1); for (k=1, #d, if (d[k], d[k]=p*=d[k])); fromdigits(d%3, 3) }
CROSSREFS
See A305458, A353826, A353828, A353830 for similar sequences.
Cf. A353825 (inverse).
Sequence in context: A130371 A130372 A353825 * A089865 A089866 A089854
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 08 2022
STATUS
approved