A361832 -id:A361832 - cp's OEIS frontend

A361833 Fixed points of A361832.

0, 1, 2, 4, 8, 12, 13, 14, 24, 25, 26, 37, 40, 43, 74, 77, 80, 111, 112, 113, 120, 121, 122, 129, 130, 131, 222, 223, 224, 231, 232, 233, 240, 241, 242, 334, 336, 341, 362, 364, 366, 387, 392, 394, 668, 670, 672, 693, 698, 700, 721, 723, 728, 1002, 1003, 1004

Offset: 1

Rémy Sigrist, Mar 26 2023

This sequence is infinite as it contains A048328.
If v is a term, then floor(v/3) is also a term.
Empirically, for any w > 0, there are A117855(w) positive terms with w ternary digits.

			A361832(12) = 12 so 12 belongs to the sequence.
A361832(11) = 15 so 11 does not belong to the sequence.

Rémy Sigrist, PARI program

Cf. A117855, A361832.

PARI
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A371635 For any number k >= 0, let T_k be the triangle with values in {-1, 0, +1} whose base corresponds to the balanced ternary expansion of k (without leading zeros) and other values, say t above u and v, satisfy t+u+v = 0 mod 3; the balanced ternary expansion of a(n) corresponds to the left border of T_n (the most significant digit being at the bottom left corner).

Original entry on oeis.org

0, 1, 3, 2, 4, 10, 8, 9, 6, 7, 5, 11, 12, 13, 30, 29, 31, 24, 23, 25, 27, 26, 28, 18, 17, 19, 21, 20, 22, 15, 14, 16, 33, 32, 34, 36, 35, 37, 39, 38, 40, 91, 89, 90, 86, 87, 88, 93, 94, 92, 73, 71, 72, 68, 69, 70, 75, 76, 74, 82, 80, 81, 77, 78, 79, 84, 85, 83

Offset: 0

Rémy Sigrist, Mar 30 2024

This sequence is a variant of A334727 and A361832.

This sequence is a self-inverse permutation of the nonnegative integers.

			For n = 42: the balanced ternary expansion of 42 is "1TTT0" (where T denotes -1), and T_42 is as follows:
         T
        0 1
       1 T 0
      0 T T 1
     1 T T T 0
So the balanced ternary expansion of a(42) is "1010T", and a(42) = 89.

Cf. A334727, A361832, A371636.

a(n) = { my (b = [], d); while (n, b = concat(d = Mod(n, 3), b); n = (n-centerlift(d)) / 3;); my (t = vector(#b)); for (i = 1, #t, t[i] = centerlift(b[1]); b = -vector(#b-1, j, b[j]+b[j+1]);); fromdigits(t, 3); }

cp's OEIS Frontend

A361833 Fixed points of A361832.

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