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A118428
Decimal expansion of heptanacci constant.
6
1, 9, 9, 1, 9, 6, 4, 1, 9, 6, 6, 0, 5, 0, 3, 5, 0, 2, 1, 0, 9, 7, 7, 4, 1, 7, 5, 4, 5, 8, 4, 3, 7, 4, 9, 6, 3, 4, 7, 9, 3, 1, 8, 9, 6, 0, 0, 5, 3, 1, 5, 7, 9, 9, 5, 2, 4, 4, 7, 8, 2, 1, 5, 3, 4, 0, 0, 9, 5, 1, 9, 8, 0, 3, 0, 9, 6, 2, 2, 1, 8, 3, 5, 6, 3, 1, 4, 1, 5, 7, 7, 0, 2, 2, 7, 1, 9, 0, 1, 7, 0, 9, 9, 1, 6
OFFSET
1,2
COMMENTS
Other roots of the equation x^7 - x^6 - ... - x - 1 see in A239566. 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^(-7) = 2, and the k-nacci constant approaches 2 when k approaches infinity (Martin Gardner). - Bernard Schott, May 07 2022
REFERENCES
Martin Gardner, The Second Scientific American Book Of Mathematical Puzzles and Diversions, "Phi: The Golden Ratio", Chapter 8, p. 101, 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, Heptanacci Number
Eric Weisstein's World of Mathematics, Heptanacci Constant
EXAMPLE
1.9919641966050350210...
MATHEMATICA
RealDigits[x/.FindRoot[x^7+Total[-x^Range[0, 6]]==0, {x, 2}, WorkingPrecision-> 110]][[1]] (* Harvey P. Dale, Dec 13 2011 *)
CROSSREFS
k-nacci constants: A001622 (Fibonacci), A058265 (tribonacci), A086088 (tetranacci), A103814 (pentanacci), A118427 (hexanacci), this sequence (heptanacci).
Sequence in context: A343367 A145280 A144667 * A166925 A178164 A216035
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Apr 27 2006
STATUS
approved