1,1

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

Stern polynomial B(25,x) = B(5*5,x) = x^3 + 3*x^2 + 2*x + 1 is irreducible, thus is not a multiple of Stern polynomial B(5, x) = 2*x + 1, and therefore 25 is included in this sequence.

Stern polynomial B(481,x) = B(13*37,x) = 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 the factors is B(13, x) = 2*x^2 + 2*x + 1 nor B(37,x) = x^3 + 5*x^2 + 4*x + 1, 481 is included in this sequence. Note that 481 is the first term that represents a reducible polynomial (i.e., is listed in A391336 rather than A391337). [Edited by Peter Munn, Dec 18 2025]

(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)); mapput(memo_for_ps, n, v); (v)));

p2r(p) = { my(v=Vecrev(Vec(p))); prod(i=1, #v, prime(i)^v[i]); };

is_A391258(n) = if(!(n%2) || 2!=bigomega(n), 0, my(f=factor(n), a = f[1, 1], b = f[#f~, 1], Pa = ps(a), Pb = if(b==a, Pa, ps(b)), Pn = ps(n)); (0!=lift(Pn % Pa) && 0!=lift(Pn % Pb)));

Setwise difference A046315 \ A391257.

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

Differs from its subsequence A391337 for the first time at n=43, where a(43) = 481, while A391337(43) = 485. See also A391336 and A389918.

Cf. also A391254.

Sequence in context: A157269 A371129 A186892 * A391337 A206075 A391254

Adjacent sequences: A391255 A391256 A391257 * A391259 A391260 A391261

nonn,changed

Antti Karttunen, Dec 07 2025

approved