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

Author

T. D. Noe, May 02 2005

Keywords

• nonn
• hard
• more

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

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

Crossrefs

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

Programs

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