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A327850 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=2, m=3. 2
83, 359, 631, 2633, 37579, 43411, 52409, 80723, 374383, 10717481, 23629421, 26528431, 44767195 (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.

LINKS

Table of n, a(n) for n=1..13.

Maciej Ulas, Strong arithmetic property of certain Stern polynomials, arXiv:1909.10844 [math.NT], 2019. See Table 4 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, 2, 3), print1(n, ", ")));

CROSSREFS

Cf. A125184 (Stern polynomials), A327848, A327849.

Sequence in context: A341338 A031433 A177099 * A061525 A293979 A340861

Adjacent sequences:  A327847 A327848 A327849 * A327851 A327852 A327853

KEYWORD

nonn,more

AUTHOR

Michel Marcus, Sep 28 2019

STATUS

approved

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Last modified June 24 21:50 EDT 2021. Contains 345433 sequences. (Running on oeis4.)