A193599 Indices n such that Padovan(n) > R^n/(2*R+3) where R is the only real root of the polynomial x^3-x-1.

0, 3, 5, 6, 8, 10, 11, 13, 16, 18, 21, 23, 24, 26, 28, 29, 31, 34, 36, 39, 41, 42, 44, 46, 47, 49, 52, 54, 55, 57, 59, 60, 62, 65, 67, 70, 72, 73, 75, 77, 78, 80, 83, 85, 88, 90, 91, 93, 95, 96, 98, 101, 103, 106, 108, 109, 111, 114, 116, 119, 121, 122, 124

Offset: 0

Author

Francesco Daddi, Jul 31 2011

Keywords

• nonn

Comments

R is plastic number (A060006).

Examples

			For n=24, Padovan(24) = 151 > 150.99309... = R^24/(2*R+3).
		

Crossrefs

Cf. A000931, A060006.

Programs

Mathematica

lim = 200; R = Solve[x^3 - x - 1 == 0, x][[1, 1, 2]]; powers = Table[Floor[R^n/(2*R + 3)], {n, 0, lim}]; p = CoefficientList[Series[(1 - x^2)/(1 - x^2 - x^3), {x, 0, lim}], x]; Select[Range[lim+1], p[[#]] > powers[[#]] &] - 1 (* T. D. Noe, Aug 01 2011 *)