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%I #31 Jan 02 2023 12:30:46
%S 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,
%T 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,
%U 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
%N Decimal expansion of heptanacci constant.
%C 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
%C 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
%D Martin Gardner, The Second Scientific American Book Of Mathematical Puzzles and Diversions, "Phi: The Golden Ratio", Chapter 8, p. 101, Simon & Schuster, NY, 1961.
%H S. Litsyn and Vladimir Shevelev, <a href="http://dx.doi.org/10.1142/S1793042105000339">Irrational Factors Satisfying the Little Fermat Theorem</a>, International Journal of Number Theory, vol.1, no.4 (2005), 499-512.
%H Vladimir Shevelev, <a href="http://list.seqfan.eu/oldermail/seqfan/2014-March/012750.html">A property of n-bonacci constant</a>, Seqfan (Mar 23 2014)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeptanacciNumber.html">Heptanacci Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeptanacciConstant.html">Heptanacci Constant</a>
%e 1.9919641966050350210...
%t RealDigits[x/.FindRoot[x^7+Total[-x^Range[0,6]]==0,{x,2}, WorkingPrecision-> 110]][[1]] (* _Harvey P. Dale_, Dec 13 2011 *)
%Y Cf. A066178, A239566.
%Y k-nacci constants: A001622 (Fibonacci), A058265 (tribonacci), A086088 (tetranacci), A103814 (pentanacci), A118427 (hexanacci), this sequence (heptanacci).
%K nonn,cons
%O 1,2
%A _Eric W. Weisstein_, Apr 27 2006
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