A191909 Decimal expansion of the limit of the square root of the ratio of consecutive Padovan numbers.

8, 6, 8, 8, 3, 6, 9, 6, 1, 8, 3, 2, 7, 0, 9, 3, 0, 1, 8, 0, 6, 5, 6, 9, 9, 6, 4, 1, 9, 1, 0, 9, 7, 2, 2, 2, 4, 7, 7, 4, 6, 5, 6, 6, 2, 0, 1, 4, 4, 9, 9, 3, 1, 6, 9, 2, 6, 0, 8, 7, 1, 9, 8, 5, 6, 1, 2, 6, 0, 2, 2, 0, 7, 5, 2, 2, 7, 7, 7, 4, 1, 1, 8, 1, 4, 2

Offset: 0

Author

Fabrice Auzanneau, Jun 19 2011

Keywords

• nonn
• cons

Comments

This is the square root of the inverse of the plastic number A060006: 1.32471795724...

This is the positive root of x^6 + x^4 - 1 = 0 and the square root of A075778.

An algebraic integer of degree 6 and minimal polynomial x^6 + x^4 - 1. - Charles R Greathouse IV, Apr 21 2016

Examples

			0.868836961832709301806569964191...
		

Links

• Wikipedia, Plastic number
• Index entries for algebraic numbers, degree 6

Crossrefs

Cf. A000931, A060006.

Programs

Mathematica

RealDigits[x/.FindRoot[x^6+x^4==1,{x,.8},WorkingPrecision->120]][[1]] (* Harvey P. Dale, Jan 17 2014 *)

PARI

polrootsreal(x^6+x^4-1)[2] \\ Charles R Greathouse IV, Apr 21 2016