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A118427 Decimal expansion of hexanacci constant. 7
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 (list; constant; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Apr 27 2006
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)