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

0,6

Links

Table of n, a(n) for n=0..90.

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.

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 *)

Prog

(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)));

Crossrefs

Cf. A125184, A277314, A277315.

Sequence in context: A072170 A368885 A294932 * A056624 A193348 A263723

Adjacent sequences: A327801 A327802 A327803 * A327805 A327806 A327807

Keyword

nonn

Author

Michel Marcus, Sep 26 2019

Status

approved