A370932 - OEIS

A370932

For any number n >= 0 with ternary expansion Sum_{i >= 0} t_i * 3^i, a(n) = Sum_{i >= 0} ((Sum_{j >= 0} (-1)^j * t_{i+j}) mod 3) * 3^i.

0, 1, 2, 5, 3, 4, 7, 8, 6, 16, 17, 15, 9, 10, 11, 14, 12, 13, 23, 21, 22, 25, 26, 24, 18, 19, 20, 50, 48, 49, 52, 53, 51, 45, 46, 47, 27, 28, 29, 32, 30, 31, 34, 35, 33, 43, 44, 42, 36, 37, 38, 41, 39, 40, 70, 71, 69, 63, 64, 65, 68, 66, 67, 77, 75, 76, 79, 80

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OFFSET

0,3

COMMENTS

In other words, the k-th ternary digit of a(n) is congruent (modulo 3) to the alternate sum of the digits to the left of (and including) the k-th ternary digit of n.

This sequence is a permutation of the nonnegative integers with inverse A071770 that preserves the number of ternary digits (A081604) and the leading ternary digit (A122586).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..19682

Index entries for sequences that are permutations of the natural numbers

FORMULA

A081604(a(n)) = A081604(n).

A122586(a(n)) = A122586(n).

EXAMPLE

For n = 42: the ternary expansion of 42 is "1120"; also:

+ 1 = 1 (mod 3)

- 1 + 1 = 0 (mod 3)

+ 1 - 1 + 2 = 2 (mod 3)

- 1 + 1 - 2 + 0 = 1 (mod 3)