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 A186891 Numbers n such that the Stern polynomial B(n,x) is irreducible. 30
 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 53, 55, 59, 61, 65, 67, 71, 73, 77, 79, 83, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 121, 125, 127, 131, 133, 137, 139, 143, 145, 149, 151, 157, 161, 163, 167, 169, 173, 175, 179, 181, 185, 191, 193, 197, 199 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 Maciej Ulas and Oliwia Ulas, On certain arithmetic properties of Stern polynomials, arXiv:1102.5109 [math.CO], 2011. FORMULA From Antti Karttunen, Mar 21 2017: (Start) A283992(a(1+n)) = n. A260443(a(1+n)) = A277318(n). (End) MATHEMATICA 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]]]]; selQ[n_] := IrreduciblePolynomialQ[ps[n]]; Join[{1}, Select[Range[200], selQ]] (* Jean-François Alcover, Nov 02 2018, translated from PARI *) PROG (PARI) ps(n)=if(n<2, n, if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2))) is(n)=polisirreducible(ps(n)) \\ Charles R Greathouse IV, Apr 07 2015 CROSSREFS Cf. A057526 (degree of Stern polynomials), A125184, A260443 (Stern polynomials). Cf. A186892 (subsequence of nonprime terms). Cf. A186893 (subsequence for self-reciprocal polynomials). Positions of 0 and 1's in A277013, Positions of 1 and 2's in A284011. Cf. A283991 (characteristic function for terms > 1). Cf. also A186886, A277190, A277318, A283992. Sequence in context: A161578 A261271 A308966 * A206074 A325559 A257688 Adjacent sequences:  A186888 A186889 A186890 * A186892 A186893 A186894 KEYWORD nonn AUTHOR T. D. Noe, Feb 28 2011 STATUS approved

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Last modified October 14 15:14 EDT 2019. Contains 328019 sequences. (Running on oeis4.)