A391341 Numbers k such that Stern polynomial B(5*k,x) is irreducible.

1, 5, 11, 13, 19, 23, 25, 29, 35, 37, 41, 43, 47, 49, 53, 59, 61, 67, 79, 83, 85, 89, 95, 97, 101, 103, 109, 115, 125, 131, 133, 139, 151, 157, 161, 163, 173, 175, 179, 181, 185, 187, 191, 193, 197, 199, 205, 209, 211, 215, 217, 227, 229, 233, 245, 251, 259, 269, 275, 281, 283, 293, 295, 301, 305, 307, 311, 313, 317

Offset

1,2

Comments

Numbers k such that A260443(5*k) is in A206284.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

{k for which A283991(5*k) = 1}.

a(n) = A391345(n) / 5.

Example

55 = 5*11, and Stern polynomial B(55,x) = x^4 + 2*x^3 + 4*x^2 + 3*x + 1 is irreducible, therefore 11 is included in this sequence.

Prog

(PARI)
memo_for_ps = Map();
ps(n) = if(n<2, n, my(v); if(mapisdefined(memo_for_ps, n, &v), v, v = if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2)); if(n%2, mapput(memo_for_ps, n, v)); (v))); \\ Only memoize on odd n...
is_A391341(n) = polisirreducible(ps(5*n));

Crossrefs

Cf. A206284, A283991, A391342 (complement), A391345.

Union of {1} and the setwise difference A391349 \ A391350.

After 1, a subsequence of A391347.

Cf. A125184, A260443 for a description of Stern polynomials.

Sequence in context: A328058 A191042 A049511 * A024900 A087490 A140565

Adjacent sequences: A391338 A391339 A391340 * A391342 A391343 A391344

Keyword

nonn

Author

Antti Karttunen, Dec 12 2025

Status

approved