A389918 Numbers m such that Stern polynomial B(m,x) has no irreducible polynomial factors that themselves are Stern polynomials. The initial a(1) = 1 is included by convention.

1, 481, 3149, 3869, 3959, 3971, 4235, 4255, 4343, 8321, 8453, 8695, 9947, 10403, 11183, 12091, 12643, 12773, 15151, 15229, 15857, 16511, 16867, 17441, 19337, 19865, 20041, 20069, 20777, 22199, 24289, 24313, 24817, 24881, 27173, 27317, 28199, 28375, 28985, 29069, 29975, 30227, 30371, 30451, 30599, 31007, 31783, 32513

Offset

1,2

Comments

Some of the products of these terms are also in this sequence, e.g., the following three ones, a(2)*a(39) = 13941785, a(5)*a(64) = 198112319 and a(8)*a(44) = 129569005 are all terms.

Question: Does this have any common terms with A391243?

Links

Antti Karttunen, Table of n, a(n) for n = 1..3001

Example

Stern polynomial B(481, x) is x^7 + 2*x^6 + 3*x^5 + 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1, which factorizes as (x^3 + x^2 + 1)(x^4 + x^3 + 2*x^2 + 2*x + 1), and because neither of factors is itself a Stern polynomial, 481 is included in this sequence.

Prog

(PARI) is_A389918(k) = (0==A391237(k));

Crossrefs

Positions of 0's in A391237.

After the initial 1, a subsequence of A389917.

Cf. A125184, A260443.

Cf. also A391241, A391243.

Sequence in context: A020271 A290338 A365657 * A254896 A165384 A365688

Adjacent sequences: A389915 A389916 A389917 * A389919 A389920 A389921

Keyword

nonn

Author

Antti Karttunen, Dec 05 2025

Status

approved