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

1, 1, 2, 2, 22, 40, 114, 12, 480, 944, 2026, 3918, 8166, 16104, 32630, 240, 131038, 260928, 524250, 1046418, 2096706, 4190168, 8388562, 16768200, 33554240, 67092432, 134216136, 268402446, 536870854, 1073672968, 2147483586, 65280, 8589928346, 17179606976, 34359737478

Offset: 1

Author

Eric W. Weisstein, Apr 28 2006

Keywords

• nonn

Comments

a(2^n) is A087046(n).

Examples

			The onsets begin at 1, 3, 1+2*sqrt(2), 1+sqrt(6), ...
		

Links

• Cheng Zhang, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Logistic Map

Crossrefs

Cf. A000740, A006876, A086178, A086180, A087046, A091517, A098587, A118452, A118453, A118746, A181906, A181907, A181909, A181910, A181911.

Programs

Mathematica

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 *)

Extensions

More terms from Cheng Zhang, Apr 02 2012