A327849 Nontrivial odd solutions n to P(n) == 1 + r*Sum_{i=1..d(n)} x^i (mod m) where P(n) is the n-th Stern polynomial, d(n) is the degree of P(n), r=1, m=3.

157, 4789, 12615, 46257, 78765, 120147, 201069, 46343011, 156666811, 1235649115, 45728246203, 78080354869, 95882561515, 775752845083

Offset

1,1

Comments

Nontrivial means solutions neither of the form 2^(k+1)-1 nor of the form 2^(k+2)-3.

Links

Table of n, a(n) for n=1..14.

Maciej Ulas, Strong arithmetic property of certain Stern polynomials, arXiv:1909.10844 [math.NT], 2019. See Table 3 p. 12.

Prog

(PARI) pol(n) = {if (n<2, return (n)); if (n%2, pol((n+1)/2) + pol((n-1)/2), x*pol(n/2)); } \\ A125184
ispow2(n) = if ((n==1) || (n==2), return (1)); my(p); isprimepower(n, &p) && (p==2);
istrivial(n) = ispow2(n+1) || ispow2(n+3);
isokrm(n, r, m) = {if ((n%2) && !istrivial(n), my(p=pol(n), d=poldegree(p)); Mod(p, m) == Mod(1+r*sum(i=1, d, x^i), m); ); }
lista(nn) = forstep(n=1, nn, 2, if (isokrm(n, 1, 3), print1(n, ", ")));

Crossrefs

Cf. A125184 (Stern polynomials), A327848, A327850.

Sequence in context: A212237 A078964 A171345 * A066823 A213469 A074220

Adjacent sequences: A327846 A327847 A327848 * A327850 A327851 A327852

Keyword

nonn,more

Author

Michel Marcus, Sep 28 2019

Status

approved