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 A346461 #19 Dec 13 2021 17:46:09
%S A346461 2,8,16,32,128,256,512,2048,4096,8192,32768,65536,131072,524288,
%T A346461 1048576,2097152,8388608,16777216,33554432,134217728,268435456,
%U A346461 536870912,2147483648,4294967296,8589934592,34359738368,68719476736,137438953472,549755813888,1099511627776
%N A346461 a(n) = 2^A042965(n+1).
%C A346461 For each n, all positive integers cannot be colored with two colors without any positive integer x being the same color as 4*x or a(n)*x.
%C A346461 A346459(a(n), 4) = 1 for all n > 1.
%C A346461 {a(n)} is the fourth row in A346460.
%H A346461 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,16).
%F A346461 a(n) = 2^(floor((4*n+1)/3)).
%F A346461 a(n) = a(n-1) * a(n-3) / a(n-4) for n > 4.
%F A346461 From _Stefano Spezia_, Sep 04 2021: (Start)
%F A346461 G.f.: 2*x*(1 + 4*x + 8*x^2)/(1 - 16*x^3).
%F A346461 a(n) = 16*a(n-3) for n > 3. (End)
%e A346461 All positive integers cannot be colored with two colors without any positive integer x being the same color as a(1)*x = 2*x or 4*x, since at least two elements of the set {2, 4, 8} have to be the same color, which violates the condition.
%t A346461 Rest@ CoefficientList[Series[2 x (1 + 4 x + 8 x^2)/(1 - 16 x^3), {x, 0, 30}], x] (* _Michael De Vlieger_, Oct 12 2021 *)
%o A346461 (PARI) A346461(n) = (1<<((4*(1+n)-3)\3)); \\ _Antti Karttunen_, Nov 11 2021
%o A346461 (Python)
%o A346461 print([2 ** ((4 * n + 1) // 3) for n in range(1, 31)])
%Y A346461 Cf. A000302, A004171, A016825, A042965, A346459, A346460.
%K A346461 nonn,easy
%O A346461 1,1
%A A346461 _M. Eren Kesim_, Sep 04 2021