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

1,1

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.

Links

Table of n, a(n) for n=1..7.

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

Example

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.

Crossrefs

Cf. A125184, A186891.

Sequence in context: A157262 A007975 A109796 * A024029 A134501 A210928

Adjacent sequences: A186883 A186884 A186885 * A186887 A186888 A186889

Keyword

nonn,more

Author

Jonathan Vos Post, Feb 28 2011

Status

approved