A186890 Numbers n such that the Stern polynomial B(n,x) is self-reciprocal.

1, 3, 7, 9, 11, 15, 27, 31, 49, 59, 63, 123, 127, 135, 177, 201, 225, 251, 255, 287, 297, 363, 377, 433, 441, 507, 511, 567, 729, 855, 945, 961, 1019, 1023, 1401, 1969, 2043, 2047, 3087, 3135, 3143, 3449, 3969, 4017, 4091, 4095, 5929, 7545, 8113, 8187, 8191

Offset: 1

Author

T. D. Noe, Feb 28 2011

Keywords

• nonn

Comments

These numbers are mentioned by Ulas and Ulas. All numbers of the form 2^k-1, 2^k-5, and (2^k-1)^2 are here.

Links

• Maciej Ulas and Oliwia Ulas, On certain arithmetic properties of Stern polynomials, arXiv:1102.5109 [math.CO], 2011.

Crossrefs

Cf. A057526 (degree of Stern polynomials), A125184 (Stern polynomials)

Programs

Mathematica

b[0]=0; b[1]=1; b[n_] := b[n] = If[EvenQ[n], x b[n/2], b[Floor[n/2]] + b[Ceiling[n/2]]]; Select[Range[10000], CoefficientList[b[#], x] == Reverse[CoefficientList[b[#], x]] &]