A318723 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 imaginary part of g(n).

0, -1, -1, 1, 1, 0, -1, -2, -2, -2, -2, -1, 2, 2, 1, 2, 3, 3, 3, 3, 2, 1, 0, 0, -2, -3, -3, -1, -1, -2, -3, -4, -4, -4, -4, -3, -3, -3, -2, -3, -4, -4, -4, -4, -3, -2, -1, -1, 4, 4, 3, 4, 5, 5, 5, 5, 4, 3, 2, 2, 5, 6, 6, 4, 4, 5, 6, 7, 7, 7, 7, 6, 6, 6, 5, 6

Offset

0,8

Comments

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

Links

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

Prog

(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)))); imag((z-1-I)/2)

Crossrefs

Cf. A318722.

Sequence in context: A248380 A090044 A036238 * A225180 A276134 A297031

Adjacent sequences: A318720 A318721 A318722 * A318724 A318725 A318726

Keyword

sign,base

Author

Rémy Sigrist, Sep 02 2018

Status

approved