A389918 - OEIS

%I #16 Dec 06 2025 21:32:15

%S 1,481,3149,3869,3959,3971,4235,4255,4343,8321,8453,8695,9947,10403,

%T 11183,12091,12643,12773,15151,15229,15857,16511,16867,17441,19337,

%U 19865,20041,20069,20777,22199,24289,24313,24817,24881,27173,27317,28199,28375,28985,29069,29975,30227,30371,30451,30599,31007,31783,32513

%N 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.

%C 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.

%C Question: Does this have any common terms with A391243?

%H Antti Karttunen, <a href="/A389918/b389918.txt">Table of n, a(n) for n = 1..3001</a>

%e 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.

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

%Y Positions of 0's in A391237.

%Y After the initial 1, a subsequence of A389917.

%Y Cf. A125184, A260443.

%Y Cf. also A391241, A391243.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 05 2025