A318705 - OEIS

A318705

For any n >= 0 with base-9 representation Sum_{k=0..w} d_k * 9^k, let g(n) = Sum_{k=0..w} s(d_k) * 3^k (where s(0) = 0, s(1+2*j) = i^j and s(2+2*j) = i^j * (1+i) for any j > 0, and i denotes the imaginary unit); a(n) is the real part of g(n).

0, 1, 1, 0, -1, -1, -1, 0, 1, 3, 4, 4, 3, 2, 2, 2, 3, 4, 3, 4, 4, 3, 2, 2, 2, 3, 4, 0, 1, 1, 0, -1, -1, -1, 0, 1, -3, -2, -2, -3, -4, -4, -4, -3, -2, -3, -2, -2, -3, -4, -4, -4, -3, -2, -3, -2, -2, -3, -4, -4, -4, -3, -2, 0, 1, 1, 0, -1, -1, -1, 0, 1, 3, 4, 4

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OFFSET

0,10

COMMENTS

See A318706 for the imaginary part of g.

See A318707 for the square of the modulus of g.

The following diagrams shows s(k) for k = 0..8 in the complex plane:

s(4) s(3) s(2)

---s(5)--s(0)--s(1)---

s(6) s(7) s(8)

The function g defines a bijection from the nonnegative integers to the Gaussian integers.

This sequence has similarities with A316657.