A186886 Least number k having exactly n prime divisors and the Stern polynomial B(k,x) is irreducible.

2, 55, 665, 6545, 85085, 1616615, 37182145

Offset: 1

Author

Jonathan Vos Post, Feb 28 2011

Keywords

• nonn
• more

Comments

Ulas and Ulas tabulate these values and conjecture 6.5, p.20, that a(n) exists for all n.

See A125184 for the Stern polynomials. See A186891 for n such that the Stern polynomial B_n(x) is irreducible.

Examples

			a(1) = 2.
a(2) = 55 = 5 * 11.
a(3) = 665 = 5 * 7 * 19.
a(4) = 6545 = 5 * 7 * 11 * 17.
a(5) = 85085 = 5 * 7 * 11 * 13 * 17.
a(6) = 1616615 = 5 * 7 * 11 * 13 * 17 * 19.
a(7) = 37182145 = 5 * 7 * 11 * 13 * 17 * 19 * 23.
		

Links

• Maciej Ulas and Oliwia Ulas, On certain arithmetic properties of Stern polynomials, arXiv:1102.5109 [math.CO], 2011.

Crossrefs

Cf. A125184, A186891.