A118428 Decimal expansion of heptanacci constant.

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

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, 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

Cf. A066178, A239566.

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

Adjacent sequences: A118425 A118426 A118427 * A118429 A118430 A118431

Keyword

nonn,cons

Author

Eric W. Weisstein, Apr 27 2006

Status

approved