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A118428 Decimal expansion of heptanacci constant. 2


%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

%H S. Litsyn and V. 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 V. Shevelev, <a href="http://list.seqfan.eu/pipermail/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.

%K nonn,cons

%O 1,2

%A _Eric W. Weisstein_, Apr 27 2006

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Last modified December 11 01:07 EST 2019. Contains 329910 sequences. (Running on oeis4.)