A118427 Decimal expansion of hexanacci constant.

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

Offset: 1

Author

Eric W. Weisstein, Apr 27 2006

Keywords

• nonn
• cons

Comments

The continued fraction expansion starts 1, 1, 59, 1, 10, 2, 1, 6, 2, 1, 6, 1, 1, 7, 1, 71, 7, 1, 6, 8, ... - R. J. Mathar, Mar 09 2012

For n>=7, round(c^prime(n)) == 1 (mod 2*prime(n)). Proof in Shevelev link. - Vladimir Shevelev, Mar 21 2014

Note that we have: c + c^(-6) = 2, and the k-nacci constant approaches 2 when k approaches infinity (Martin Gardner). - Bernard Schott, May 06 2022

Examples

			1.9835828434243263303...
		

References

• Martin Gardner, The Second Scientific American Book Of Mathematical Puzzles and Diversions, "Phi: The Golden Ratio", Chapter 8, Simon & Schuster, NY, 1961.

Links

• S. Litsyn and Vladimir Shevelev, Irrational Factors Satisfying the Little Fermat Theorem, International Journal of Number Theory, vol.1, no.4 (2005), 499-512.
• Vladimir Shevelev, A property of n-bonacci constant, Seqfan (Mar 23 2014)
• Eric Weisstein's World of Mathematics, Hexanacci Number
• Eric Weisstein's World of Mathematics, Hexanacci Constant
• Eric Weisstein's World of Mathematics, Hexanacci Number
• Index entries for algebraic numbers, degree 6.

Crossrefs

Cf. A001592.

k-nacci constants: A001622 (Fibonacci), A058265 (tribonacci), A086088 (tetranacci), A103814 (pentanacci), this sequence (hexanacci), A118428 (heptanacci).

Programs

Mathematica

RealDigits[ Root[ x^6 - x^5 - x^4 - x^3 - x^2 - x - 1, 2] , 10, 105] // First (* Jean-François Alcover, Feb 07 2013 *)