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

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)))

Crossrefs

Cf. A318705, A318706.

Sequence in context: A336336 A168580 A356206 * A363228 A235726 A060938

Adjacent sequences: A318704 A318705 A318706 * A318708 A318709 A318710

Keyword

nonn,base,look

Author

Rémy Sigrist, Sep 01 2018

Status

approved