A389912 Prime-factorization representation of irreducible (non-constant) Stern-polynomials B(m,x), listed in ascending order.

3, 6, 18, 30, 270, 450, 630, 2310, 6750, 9450, 15750, 22050, 90090, 510510, 727650, 2668050, 3543750, 4961250, 18191250, 25467750, 29099070

Offset

1,1

Comments

See A260443 for how Stern-polynomials can be encoded with the prime factorization of natural numbers.

Numbers k > 2 such that A277333(k) is in A186891.

Links

Table of n, a(n) for n=1..21.

Maciej Ulas and Oliwia Ulas, On certain arithmetic properties of Stern polynomials, arXiv:1102.5109 [math.CO], 2011. (See Conjecture 6.4. on p. 20)

Formula

{k such that A389449(k)*A389911(k) = 1}.

{k such that A389449(k)*A389913(k) = 1}.

Prog

(PARI) is_A389912(n) = (A389449(n) && A389911(n));
(PARI) is_A389912(n) = { my(k); if(3==n, 1, if(n%2 || (omega(n) < A061395(n)), 0, k = A048675(n); if((A260443(k) == n), A283991(k), 0))); };

Crossrefs

Sequence A277318 sorted into ascending order.

Intersection of A206284 and A260442.

Intersection of A260442 and A389914.

After the initial 3, subsequence of A055932.

Cf. A186891, A260443, A277317 (conjectured subsequence), A277333, A283991, A389449, A389911, A389913.

Sequence in context: A352786 A117863 A103100 * A277317 A277318 A277316

Adjacent sequences: A389909 A389910 A389911 * A389913 A389914 A389915

Keyword

nonn,more

Author

Antti Karttunen, Dec 03 2025

Status

approved