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 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 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

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