login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 2
19, 181, 29899, 40123, 44659, 72361, 87211, 183439, 373465, 2965429, 5073589, 17484211, 44733781, 165459277, 1381288843, 2572135705, 2833893901 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,more
AUTHOR
Michel Marcus, Sep 28 2019
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 12 22:48 EDT 2024. Contains 371639 sequences. (Running on oeis4.)