A350775 The balanced ternary expansion of a(n) is obtained by multiplying adjacent digits in the balanced ternary expansion of n: a(Sum_{k >= 0} t_k * 3^k) = Sum_{k >= 0} t_k * t_{k+1} * 3^k (with -1 <= t_k <= 1 for any k >= 0).

0, 0, -1, 0, 1, -2, -3, -4, 0, 0, 0, 2, 3, 4, -5, -6, -7, -9, -9, -9, -13, -12, -11, 1, 0, -1, 0, 0, 0, -1, 0, 1, 7, 6, 5, 9, 9, 9, 11, 12, 13, -14, -15, -16, -18, -18, -18, -22, -21, -20, -26, -27, -28, -27, -27, -27, -28, -27, -26, -38, -39, -40, -36, -36

Offset: 0

Author

Rémy Sigrist, Jan 15 2022

Keywords

• sign
• base

Comments

This sequence is to balanced ternary what A048735 is to binary, or what A330633 is to decimal.

Examples

			The first terms, in decimal and in balanced ternary, are:
  n   a(n)  bter(n)  bter(a(n))
  --  ----  -------  ----------
   0     0        0           0
   1     0        1           0
   2    -1       1T           T
   3     0       10           0
   4     1       11           1
   5    -2      1TT          T1
   6    -3      1T0          T0
   7    -4      1T1          TT
   8     0      10T           0
   9     0      100           0
  10     0      101           0
  11     2      11T          1T
  12     3      110          10
  13     4      111          11
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..9841

Crossrefs

Cf. A048735, A059095, A330633, A350776.

Programs

PARI

a(n) = { my (v=0, p=0, d); for (x=-1, oo, if (n==0, return (v), d=[0, 1, -1][1+n%3]; v+=p*d*3^x; n=(n-d)/3; p=d)) }

Formula

a(n) = 0 iff n belongs to A350776.