cp's OEIS Frontend

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.

A118454 Algebraic degree of the onset of the logistic map n-bifurcation.

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%I A118454 #21 Aug 19 2025 03:54:14
%S A118454 1,1,2,2,22,40,114,12,480,944,2026,3918,8166,16104,32630,240,131038,
%T A118454 260928,524250,1046418,2096706,4190168,8388562,16768200,33554240,
%U A118454 67092432,134216136,268402446,536870854,1073672968,2147483586,65280,8589928346,17179606976,34359737478
%N A118454 Algebraic degree of the onset of the logistic map n-bifurcation.
%C A118454 a(2^n) is A087046(n).
%H A118454 Cheng Zhang, <a href="/A118454/b118454.txt">Table of n, a(n) for n = 1..1000</a>
%H A118454 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LogisticMap.html">Logistic Map</a>
%e A118454 The onsets begin at 1, 3, 1+2*sqrt(2), 1+sqrt(6), ...
%t A118454 degRp[n_] := Sum[MoebiusMu[n/d] 2^(d - 1), {d, Divisors[n]}]; degRo[n_] := degRp[n]*2 - Sum[EulerPhi[n/d] degRp[d], {d, Divisors[n]}]; Table[If[n <= 2, 1, 2 If[2^Round[Log2[n]] == n, degRp[n/2], degRo[n]]], {n, 1, 35}] (* _Cheng Zhang_, Apr 02 2012 *)
%Y A118454 Cf. A000740, A006876, A086178, A086180, A087046, A091517, A098587, A118452, A118453, A118746, A181906, A181907, A181909, A181910, A181911.
%K A118454 nonn
%O A118454 1,3
%A A118454 _Eric W. Weisstein_, Apr 28 2006
%E A118454 More terms from _Cheng Zhang_, Apr 02 2012