A380180 Irregular table T(n, k), n >= 0, k = 1..2^A005812(n); the n-th row lists the integers m (possibly negative) such that the nonzero digits in the balanced ternary expansion of m appear in the balanced ternary expansion of n.

0, 0, 1, -1, 0, 2, 3, 0, 3, 0, 1, 3, 4, -4, -3, -1, 0, 5, 6, 8, 9, -3, 0, 6, 9, -3, -2, 0, 1, 6, 7, 9, 10, -1, 0, 8, 9, 0, 9, 0, 1, 9, 10, -1, 0, 2, 3, 8, 9, 11, 12, 0, 3, 9, 12, 0, 1, 3, 4, 9, 10, 12, 13, -13, -12, -10, -9, -4, -3, -1, 0, 14, 15, 17, 18, 23, 24, 26, 27

Offset: 0

Author

Rémy Sigrist, Jan 15 2025

Keywords

• sign
• base
• tabf

Comments

Every integer appears infinitely many times in the sequence.

See A368239 (resp. A380181) for the nonnegative values (resp. the nonpositive values, negated) in order of appearance in the present sequence.

Examples

			Irregular table T(n, k) begins:
  n   n-th row
  --  -------------------------
   0  0
   1  0, 1
   2  -1, 0, 2, 3
   3  0, 3
   4  0, 1, 3, 4
   5  -4, -3, -1, 0, 5, 6, 8, 9
   6  -3, 0, 6, 9
   7  -3, -2, 0, 1, 6, 7, 9, 10
   8  -1, 0, 8, 9
   9  0, 9
  10  0, 1, 9, 10
  11  -1, 0, 2, 3, 8, 9, 11, 12
  12  0, 3, 9, 12
.
Irregular table T(n, k) begins in balanced ternary:
  n    n-th row
  ---  --------------------------------
    0  0
    1  0, 1
   1T  T, 0, 1T, 10
   10  0, 10
   11  0, 1, 10, 11
  1TT  TT, T0, T, 0, 1TT, 1T0, 10T, 100
  1T0  T0, 0, 1T0, 100
  1T1  T0, T1, 0, 1, 1T0, 1T1, 100, 101
  10T  T, 0, 10T, 100
  100  0, 100
  101  0, 1, 100, 101
  11T  T, 0, 1T, 10, 10T, 100, 11T, 110
  110  0, 10, 100, 110
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..4688 (rows for n = 0..3^5 flattened)
• Wikipedia, Balanced ternary

Crossrefs

See A380123 for a similar sequence.

Cf. A005812, A060372, A060373, A368239, A380181.

Programs

PARI

row(n) = { my (r = [0], d, t = 1); while (n, d = centerlift(Mod(n, 3)); if (d, r = concat(r, [v + d*t | v <- r]);); n = (n-d)/3; t *= 3;); vecsort(r); }

Formula

T(n, 1) = - A060373(n).

T(n, 2^A005812(n)) = A060372(n).