A328749 a(n) = Sum_{k = 0..w and t_k > 0} (-1)^t_k * 2^k, where Sum_{k = 0..w} t_k * 3^k is the ternary representation of n.

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

Offset

0,4

Comments

Every integer appears in the sequence.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6561

Formula

a(n) = 0 iff n = 0.

a(n) > 0 iff n belongs to A157671.

a(n) < 0 iff n belongs to A132141.

a(A004488(n)) = -a(n).

Example

a(42) = a(1*3^3 + 1*3^2 + 2*3^1) = -2^3 - 2^2 + 2^1 = -10.

Prog

(PARI) a(n) = my (d=Vecrev(digits(n, 3))); sum(i=1, #d, if (d[i], (2^i) * (-1)^d[i], 0))/2
(Python)
from sympy.ntheory.factor_ import digits
def A328749(n): return sum((-(1<<i) if j&1 else 1<<i) for i, j in enumerate(digits(n, 3)[-1:0:-1]) if j>0) # Chai Wah Wu, Apr 12 2023

Crossrefs

Cf. A004488, A132141, A157671, A328728.

Sequence in context: A005680 A036582 A260451 * A036848 A289585 A128864

Adjacent sequences: A328746 A328747 A328748 * A328750 A328751 A328752

Keyword

sign,base

Author

Rémy Sigrist, Oct 27 2019

Status

approved