A353174 Irregular table T(n, k), n >= 0, k = 0..A352502(n-1); the n-th row lists in ascending order the numbers k in 0..n such that k and n-k can be added without carries in balanced ternary.

0, 0, 1, 0, 2, 0, 1, 2, 3, 0, 1, 3, 4, 0, 5, 0, 1, 5, 6, 0, 1, 6, 7, 0, 2, 3, 5, 6, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 3, 4, 6, 7, 9, 10, 0, 2, 3, 8, 9, 11, 0, 1, 2, 3, 4, 8, 9, 10, 11, 12, 0, 1, 3, 4, 9, 10, 12, 13, 0, 14, 0, 1, 14, 15, 0, 1, 15, 16, 0, 2, 3, 14, 15, 17

Offset

0,5

Comments

Two integers can be added without carries in balanced ternary if they have no equal nonzero digit at the same position.

This sequence has connections with A295989; here we work with balanced ternary, there with binary.

The set of points {(n, T(n, k))} has interesting fractal features, with voids in the form of Koch snowflakes (see illustration in Links section).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8768 (rows for n = 0..3^5 flattened)

Rémy Sigrist, Scatterplot of (n, T(n, k)) for n <= 3^6 on a hexagonal lattice

Wikipedia, Balanced ternary

Wikipedia, Hexaflake.

Formula

T(n, 0) = 0.

T(n, A352502(n-1)) = n.

Example

Irregular table T(n, k) begins:
    0: [0]
    1: [0, 1]
    2: [0, 2]
    3: [0, 1, 2, 3]
    4: [0, 1, 3, 4]
    5: [0, 5]
    6: [0, 1, 5, 6]
    7: [0, 1, 6, 7]
    8: [0, 2, 3, 5, 6, 8]
    9: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Prog

(PARI) ok(u, v) = { while (u && v, my (uu=[0, +1, -1][1+u%3], vv=[0, +1, -1][1+v%3]); if (abs(uu+vv)>1, return (0)); u=(u-uu)/3; v=(v-vv)/3); return (1) }
row(n) = select(k -> ok(n-k, k), [0..n])

Crossrefs

Cf. A059095, A295989, A352502.

Sequence in context: A293377 A159880 A289251 * A233292 A108456 A089107

Adjacent sequences: A353171 A353172 A353173 * A353175 A353176 A353177

Keyword

nonn,base

Author

Rémy Sigrist, Apr 28 2022

Status

approved