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A186891 Numbers n such that the Stern polynomial B(n,x) is irreducible.

%I A186891 #30 Nov 03 2018 12:15:26
%S A186891 1,2,3,5,7,11,13,17,19,23,25,29,31,37,41,43,47,53,55,59,61,65,67,71,
%T A186891 73,77,79,83,89,91,95,97,101,103,107,109,113,115,121,125,127,131,133,
%U A186891 137,139,143,145,149,151,157,161,163,167,169,173,175,179,181,185,191,193,197,199
%N A186891 Numbers n such that the Stern polynomial B(n,x) is irreducible.
%C A186891 Ulas and Ulas conjecture that all primes are here. The nonprime n are in A186892. See A186886 for the least number having n prime factors.
%H A186891 Charles R Greathouse IV, <a href="/A186891/b186891.txt">Table of n, a(n) for n = 1..10000</a>
%H A186891 Maciej Ulas and Oliwia Ulas, <a href="http://arxiv.org/abs/1102.5109">On certain arithmetic properties of Stern polynomials</a>, arXiv:1102.5109 [math.CO], 2011.
%F A186891 From _Antti Karttunen_, Mar 21 2017: (Start)
%F A186891 A283992(a(1+n)) = n.
%F A186891 A260443(a(1+n)) = A277318(n).
%F A186891 (End)
%t A186891 ps[n_] := ps[n] = If[n<2, n, If[OddQ[n], ps[Quotient[n, 2]] + ps[Quotient[n, 2] + 1], x ps[Quotient[n, 2]]]];
%t A186891 selQ[n_] := IrreduciblePolynomialQ[ps[n]];
%t A186891 Join[{1}, Select[Range[200], selQ]] (* _Jean-François Alcover_, Nov 02 2018, translated from PARI *)
%o A186891 (PARI) ps(n)=if(n<2, n, if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2)))
%o A186891 is(n)=polisirreducible(ps(n)) \\ _Charles R Greathouse IV_, Apr 07 2015
%Y A186891 Cf. A057526 (degree of Stern polynomials), A125184, A260443 (Stern polynomials).
%Y A186891 Cf. A186892 (subsequence of nonprime terms).
%Y A186891 Cf. A186893 (subsequence for self-reciprocal polynomials).
%Y A186891 Positions of 0 and 1's in A277013, Positions of 1 and 2's in A284011.
%Y A186891 Cf. A283991 (characteristic function for terms > 1).
%Y A186891 Cf. also A186886, A277190, A277318, A283992.
%K A186891 nonn
%O A186891 1,2
%A A186891 _T. D. Noe_, Feb 28 2011