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A318707

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 square of the modulus of g(n).

0, 1, 2, 1, 2, 1, 2, 1, 2, 9, 16, 17, 10, 5, 4, 5, 10, 17, 18, 25, 32, 25, 20, 13, 8, 13, 20, 9, 10, 17, 16, 17, 10, 5, 4, 5, 18, 13, 20, 25, 32, 25, 20, 13, 8, 9, 4, 5, 10, 17, 16, 17, 10, 5, 18, 13, 8, 13, 20, 25, 32, 25, 20, 9, 10, 5, 4, 5, 10, 17, 16, 17

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OFFSET

0,3

COMMENTS

See A318705 for the real part of g and additional comments.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..6560

FORMULA

a(n) = A318705(n)^2 + A318706(n)^2.

a(9 * k) = 9 * a(k) for any k >= 0.

PROG

(PARI) a(n) = my (d=Vecrev(digits(n, 9))); norm(sum(k=1, #d, if (d[k], 3^(k-1)*I^floor((d[k]-1)/2)*(1+I)^((d[k]-1)%2), 0)))