cp's OEIS Frontend

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

%I A290538 #19 May 10 2025 09:02:42
%S A290538 0,1,4,2,9,8,5,4,16,18,13,16,10,10,5,8,25,32,25,36,20,26,17,32,17,20,
%T A290538 13,20,10,5,16,36,50,41,64,34,50,37,72,29,40,29,52,34,25,64,26,34,25,
%U A290538 40,26,17,40,9,20,10,9,32,49,72,61,100,52,82,65,128,45,68
%N A290538 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 square of the norm of the n-th term of S.
%C A290538 See A290536 for the real part of the n-th term of S and additional comments.
%C A290538 See A290537 for the imaginary part of the n-th term of S.
%C A290538 a(n) tends to infinity as n tends to infinity.
%H A290538 Rémy Sigrist, <a href="/A290538/b290538.txt">Table of n, a(n) for n = 1..10000</a>
%H A290538 Rémy Sigrist, <a href="/A290538/a290538.gp.txt">PARI program for A290538</a>
%F A290538 a(n) = A290536(n)^2 + A290537(n)^2.
%e A290538 S(1) = 0 by definition; so a(1) = 0.
%e A290538 S(1)+1 = 1 has not yet occurred; so S(2) = 1 and a(2) = 1.
%e A290538 S(1)*(i+i) = 0 has already occurred.
%e A290538 S(2)+1 = 2 has not yet occurred; so S(3) = 2 and a(3) = 4.
%e A290538 S(2)*(1+i) = 1+i has not yet occurred; so S(4) = 1+i and a(4) = 2.
%e A290538 S(3)+1 = 3 has not yet occurred; so S(5) = 3 and a(5) = 9.
%o A290538 (PARI) \\ See Links section.
%Y A290538 Cf. A290536, A290537.
%K A290538 nonn,look
%O A290538 1,3
%A A290538 _Rémy Sigrist_, Aug 05 2017