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A106275 Numbers n for which the absolute value of the discriminant of the polynomial x^n - x^(n-1) -...- x - 1 is a prime times 2^k for some k >=0. 1
2, 3, 4, 5, 6, 7, 21, 26, 99, 158, 405 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This polynomial is the characteristic polynomial of the Fibonacci and Lucas n-step recursions. Are the n-step recursions different -- in some way -- for the values of n that yield a prime*2^k discriminant? No other n < 10000.

REFERENCES

Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257.  Mathematical Reviews, MR2312537.  Zentralblatt MATH, Zbl 1133.11012.

LINKS

Table of n, a(n) for n=1..11.

Eric Weisstein's World of Mathematics, Fibonacci n-Step

CROSSREFS

Cf. A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1).

Sequence in context: A010354 A070759 A282138 * A303368 A031054 A342728

Adjacent sequences:  A106272 A106273 A106274 * A106276 A106277 A106278

KEYWORD

hard,more,nonn

AUTHOR

T. D. Noe, May 02 2005

STATUS

approved

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Last modified September 17 06:16 EDT 2021. Contains 347478 sequences. (Running on oeis4.)