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 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. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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: A275019 A119387 A055941 * A272569 A068076 A138498 Adjacent sequences:  A290534 A290535 A290536 * A290538 A290539 A290540 KEYWORD sign,look AUTHOR Rémy Sigrist, Aug 05 2017 STATUS approved

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Last modified December 14 17:41 EST 2019. Contains 329979 sequences. (Running on oeis4.)