A318724 Let f(0) = 0 and f(t*4^k + u) = i^t * ((1+i) * 2^k - f(u)) for any t in {1, 2, 3} and k >= 0 and u such that 0 <= u < 4^k (i denoting the imaginary unit); for any n >= 0, let g(n) = (f(A042968(n)) - 1 - i) / 2; a(n) is the square of the modulus of g(n).

1, 2, 1, 2, 5, 4, 5, 8, 5, 4, 5, 2, 8, 13, 10, 5, 10, 13, 18, 25, 20, 17, 16, 9, 13, 18, 13, 10, 17, 20, 25, 32, 25, 20, 17, 10, 10, 13, 8, 9, 16, 17, 20, 25, 18, 13, 10, 5, 32, 41, 34, 25, 34, 41, 50, 61, 52, 45, 40, 29, 29, 40, 45, 20, 17, 26, 37, 50, 53, 58

Offset: 0

Author

Rémy Sigrist, Sep 02 2018

Keywords

• nonn
• base
• look

Comments

See A318722 for the real part of g and additional comments.

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..12287

Crossrefs

Cf. A042968, A048647, A318722, A318723.

Programs

PARI

a(n) = my (d=Vecrev(digits(1+n+n\3,4)), z=0); for (k=1, #d, if (d[k], z = I^d[k] * (-z + (1+I) * 2^(k-1)))); norm((z-1-I)/2)

Formula

a(n) = A318722(n)^2 + A318723(n)^2.

If A048647(A042968(m)) = A042968(n), then a(m) = a(n).