A327848 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=0, m=3.

19, 181, 29899, 40123, 44659, 72361, 87211, 183439, 373465, 2965429, 5073589, 17484211, 44733781, 165459277, 1381288843, 2572135705, 2833893901

Offset

1,1

Comments

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

Sequence is infinite as it includes the infinite subsequence h(n) = 2*(2^(2*n)-1)*(2^(2*n+1) + 1)/3 + 1. See link.

Links

Table of n, a(n) for n=1..17.

Maciej Ulas, Strong arithmetic property of certain Stern polynomials, arXiv:1909.10844 [math.NT], 2019. See Table 2 p. 11.

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, 0, 3), print1(n, ", ")));

Crossrefs

Cf. A125184 (Stern polynomials), A327849, A327850.

Sequence in context: A126540 A008419 A211866 * A034273 A193575 A161512

Adjacent sequences: A327845 A327846 A327847 * A327849 A327850 A327851

Keyword

nonn,more

Author

Michel Marcus, Sep 28 2019

Status

approved