A327804 Leading coefficient of the n-th Stern polynomial.

0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 3, 2, 3, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 2, 2, 3, 1, 1, 2, 1, 1, 1, 1, 1, 3, 2, 3, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 4, 3, 5, 2, 2, 2, 2, 2, 5, 3, 4, 1, 1, 1, 1, 2

Offset: 0

Author

Michel Marcus, Sep 26 2019

Keywords

• nonn

Links

• A. Schinzel, The leading coefficients of Stern polynomials, in: From Arithmetic to Zeta-Functions: Number Theory in Memory of Wolfgang Schwarz (J. Sander et al., eds.), Springer, 2016, 427-434.

Crossrefs

Cf. A125184, A277314, A277315.

Programs

Mathematica

B[0, ] = 0; B[1, ] = 1; B[n_, t_] := B[n, t] = If[EvenQ[n], t B[n/2, t], B[1 + (n-1)/2, t] + B[(n-1)/2, t]];
a[n_] := Coefficient[B[n, t], t, Exponent[B[n, t], t]]; a[0] = 0;
a /@ Range[0, 90] (* Jean-François Alcover, Sep 26 2019, from A125184 *)

PARI

pol(n) = {if (n<2, return (n)); if (n%2, pol((n+1)/2) + pol((n-1)/2), x*pol(n/2));}
a(n) = my(p=pol(n)); if (p==0, 0, polcoef(p, poldegree(p)));