A118427 - OEIS

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

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OFFSET

1,2

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

REFERENCES

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

LINKS

Table of n, a(n) for n=1..105.

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

EXAMPLE

1.9835828434243263303...

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 *)

CROSSREFS

Cf. A001592.

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

Sequence in context: A255251 A363633 A224236 * A199170 A155532 A086306

Adjacent sequences: A118424 A118425 A118426 * A118428 A118429 A118430

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Apr 27 2006

STATUS

approved