A290537 Let S be the sequence generated by these rules: 0 is in S, and if z is in S, then z + 1 and z * (1+i) are in S (where i denotes the imaginary unit), and duplicates are deleted as they occur; a(n) = the imaginary part of the n-th term of S.

0, 0, 0, 1, 0, 2, 1, 2, 0, 3, 2, 4, 1, 3, 2, 2, 0, 4, 3, 6, 2, 5, 4, 4, 1, 4, 3, 4, 3, 2, 0, 0, 5, 4, 8, 3, 7, 6, 6, 2, 6, 5, 6, 5, 4, 0, 1, 5, 4, 6, 5, 4, 2, 3, 2, 1, 0, -4, 0, 6, 5, 10, 4, 9, 8, 8, 3, 8, 7, 8, 7, 6, 0, 2, 7, 6, 8, 7, 6, 2, 5, 2, 1, 0, -8, 1

Offset

1,6

Comments

See A290536 for the real part of the n-th term of S and additional comments.

See A290538 for the square of the norm of the n-th term of S.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A290537

Example

S(1) = 0 by definition; so a(1) = 0.
S(1)+1 = 1 has not yet occurred; so S(2) = 1 and a(2) = 0.
S(1)*(i+i) = 0 has already occurred.
S(2)+1 = 2 has not yet occurred; so S(3) = 2 and a(3) = 0.
S(2)*(1+i) = 1+i has not yet occured; so S(4) = 1+i and a(4) = 1.
S(3)+1 = 3 has not yet occurred; so S(5) = 3 and a(5) = 0.

Prog

(PARI) See Links section.

Crossrefs

Cf. A290536, A290538.

Sequence in context: A347696 A365385 A366788 * A377087 A272569 A344788

Adjacent sequences: A290534 A290535 A290536 * A290538 A290539 A290540

Keyword

sign,look

Author

Rémy Sigrist, Aug 05 2017

Status

approved