This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A272636 #40 Mar 03 2024 22:24:50
%S A272636 0,1,1,2,3,5,2,7,1,2,3,5,2,7,1,2,3,5,2,7,1,2,3,5,2,7,1,2,3,5,2,7,1,2,
%T A272636 3,5,2,7,1,2,3,5,2,7,1,2,3,5,2,7,1,2,3,5,2,7,1,2,3,5,2,7,1,2,3,5,2,7,
%U A272636 1,2,3,5,2,7,1,2,3,5,2,7,1,2,3,5,2,7,1,2,3,5,2,7,1,2,3,5,2,7,1,2,3,5,2,7,1,2,3,5,2,7,1,2,3,5,2,7
%N A272636 a(0)=0, a(1)=1; thereafter a(n) = squarefree part of a(n-1)+a(n-2).
%C A272636 Periodic with period {1,2,3,5,2,7}.
%C A272636 _James Propp_, in a posting to the Math Fun list, asks if every sequence of positive numbers satisfying the same recurrence will eventually merge with this sequence (as A272638 does). The answer is no, Fred W. Helenius found infinitely many counterexamples, including A272637. See A272639 for other counterexamples which start 1,x.
%C A272636 Other counterexamples found by Helenius include [n, 2n, 3n, 5n, 2n, 7n] (period 6) where n is any squarefree positive integer coprime to 210 = 2*3*5*7.
%H A272636 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 1).
%t A272636 {0, 1}~Join~LinearRecurrence[{0, 0, 0, 0, 0, 1}, {1, 2, 3, 5, 2, 7}, 120] (* _Jean-François Alcover_, Nov 16 2019 *)
%o A272636 (Python)
%o A272636 from sympy.ntheory.factor_ import core
%o A272636 l=[0, 1]
%o A272636 for n in range(2, 101):
%o A272636 l.append(core(l[n - 1] + l[n - 2]))
%o A272636 print(l) # _Indranil Ghosh_, Jun 03 2017
%Y A272636 Cf. A007913 (squarefree part of n), A000045, A272637, A272638, A272639.
%Y A272636 See A165911 for a similar sequence.
%Y A272636 See also A214674, A214892-A214898.
%K A272636 nonn
%O A272636 0,4
%A A272636 _N. J. A. Sloane_, May 05 2016