A328728 -id:A328728 - cp's OEIS frontend

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

Rémy Sigrist, Oct 27 2019

Every integer appears in the sequence.

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

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

Cf. A004488, A132141, A157671, A328728.

a(n) = my (d=Vecrev(digits(n,3))); sum(i=1, #d, if (d[i], (2^i) * (-1)^d[i], 0))/2

from sympy.ntheory.factor_ import digits
def A328749(n): return sum((-(1<0) # Chai Wah Wu, Apr 12 2023

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).

A362090 a(n) = A328749(A362089(n)).

Original entry on oeis.org

0, -1, 1, -2, -5, -3, 2, 3, 5, -4, -9, -7, -10, -21, -19, -6, -13, -11, 4, 7, 9, 6, 11, 13, 10, 19, 21, -8, -17, -15, -18, -37, -35, -14, -29, -27, -20, -41, -39, -42, -85, -83, -38, -77, -75, -12, -25, -23, -26, -53, -51, -22, -45, -43, 8, 15, 17, 14, 27, 29

Offset: 0

Rémy Sigrist, Apr 08 2023

Every integer appears once in the sequence.

			For n = 5, the base-3 expansion of 5 is "12", so the base-3 expansion of A362089(5) is "102", and a(5) = -2^2 + 2^0 = -3.

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

Cf. A328728, A328749, A362089.

a(n) = { if (n==0, 0, n%3, 4*a(n\3) + (-1)^(n%3), 2*a(n/3)); }

from gmpy2 import digits
def A362090(n): return sum((-(1<Chai Wah Wu, Apr 12 2023

cp's OEIS Frontend

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.

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