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 A140590 #11 Jul 12 2025 21:32:10
%S A140590 3,2,9,5,33,17,129,65,513,257,2049,1025,8193,4097,32769,16385,131073,
%T A140590 65537,524289,262145,2097153,1048577,8388609,4194305,33554433,
%U A140590 16777217,134217729,67108865,536870913,268435457,2147483649,1073741825,8589934593,4294967297,34359738369
%N A140590 Exchange successive pairs of terms of A000051.
%H A140590 Andrew Howroyd, <a href="/A140590/b140590.txt">Table of n, a(n) for n = 0..1000</a>
%H A140590 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-4).
%F A140590 From _Andrew Howroyd_, Jan 03 2020: (Start)
%F A140590 a(n) = 2^(n + (-1)^n) + 1.
%F A140590 a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) for n >= 3.
%F A140590 G.f.: (3 - x - 5*x^2)/((1 - x)*(1 - 2*x)*(1 + 2*x)). (End)
%t A140590 LinearRecurrence[{1,4,-4},{3,2,9},35] (* or *) CoefficientList[Series[(3 - x - 5*x^2)/((1 - x)*(1 - 2*x)*(1 + 2*x)),{x,0,34}],x] (* or *) a[n_]:= 2^(n + (-1)^n) + 1;Array[a,35,0] (* _James C. McMahon_, Jul 12 2025 *)
%o A140590 (PARI) a(n)={(1<<bitxor(n,1)) + 1} \\ _Andrew Howroyd_, Jan 03 2020
%o A140590 (PARI) Vec((3 - x - 5*x^2)/((1 - x)*(1 - 2*x)*(1 + 2*x)) + O(x^40)) \\ _Andrew Howroyd_, Jan 03 2020
%Y A140590 Cf. A000051.
%K A140590 nonn,easy
%O A140590 0,1
%A A140590 _Paul Curtz_, Jul 06 2008
%E A140590 Terms a(16) and beyond from _Andrew Howroyd_, Jan 03 2020