A106275 Numbers k for which the absolute value of the discriminant of the polynomial x^k - x^(k-1) - ... - x - 1 is a prime times 2^m for some m >= 0.

2, 3, 4, 5, 6, 7, 21, 26, 99, 158, 405

Offset

1,1

Comments

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

Links

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

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

Prog

(PARI) f(n) = poldisc('x^n-sum(k=0, n-1, 'x^k)); \\ A106273
isok(k) = my(x=abs(f(k))); ispseudoprime(x) || ispseudoprime(x/2^valuation(x, 2)); \\ Michel Marcus, Mar 26 2024

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

nonn,hard,more,changed

Author

T. D. Noe, May 02 2005

Status

approved