cp's OEIS Frontend

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.

%I A290537 #18 May 10 2025 09:02:36
%S A290537 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,
%T A290537 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,
%U A290537 8,7,8,7,6,0,2,7,6,8,7,6,2,5,2,1,0,-8,1
%N 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.
%C A290537 See A290536 for the real part of the n-th term of S and additional comments.
%C A290537 See A290538 for the square of the norm of the n-th term of S.
%H A290537 Rémy Sigrist, <a href="/A290537/b290537.txt">Table of n, a(n) for n = 1..10000</a>
%H A290537 Rémy Sigrist, <a href="/A290537/a290537.gp.txt">PARI program for A290537</a>
%e A290537 S(1) = 0 by definition; so a(1) = 0.
%e A290537 S(1)+1 = 1 has not yet occurred; so S(2) = 1 and a(2) = 0.
%e A290537 S(1)*(i+i) = 0 has already occurred.
%e A290537 S(2)+1 = 2 has not yet occurred; so S(3) = 2 and a(3) = 0.
%e A290537 S(2)*(1+i) = 1+i has not yet occurred; so S(4) = 1+i and a(4) = 1.
%e A290537 S(3)+1 = 3 has not yet occurred; so S(5) = 3 and a(5) = 0.
%o A290537 (PARI) \\ See Links section.
%Y A290537 Cf. A290536, A290538.
%K A290537 sign,look
%O A290537 1,6
%A A290537 _Rémy Sigrist_, Aug 05 2017