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 A078598 Primes p for which one of the two factors in the factorization of the polynomial Sum_{i=0..p-1} p^i*x^(2i) has only positive coefficients. 0
 5, 13, 29, 37, 61, 101, 109, 157, 181, 229, 277, 349, 373, 421, 541, 613, 661, 709, 757, 829, 1021, 1069, 1093, 1117, 1213, 1381, 1429, 1453, 1549, 1621, 1669, 1741, 1789, 1933, 2029, 2053, 2221 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This polynomial factors iff p == 1 mod 4, but the positivity behavior seems restricted to p == 5 mod 8 with 149 as the first exception. LINKS EXAMPLE For p=5 we have 625x^8+125x^6+25x^4+5x^2+1=(25x^4+25x^3+15x^2+5x+1)(25x^4-25x^3+15x^2-5x+1) PROG (PARI) posipoly(pol) = {for (i=1, poldegree(pol), if (polcoeff(pol, i) <0, return(0)); ); return (1); } lista(n) = {forprime(p=3, n, fp = factor(sum(i=0, p-1, p^i*x^(2*i))); if (matsize(fp) == [2, 2], if (posipoly(fp[2, 1]) || posipoly(fp[1, 1]), print1(p, ", ")); ); ); } \\ Michel Marcus, Apr 14 2013 CROSSREFS Sequence in context: A213050 A216822 A217466 * A155054 A158756 A185086 Adjacent sequences:  A078595 A078596 A078597 * A078599 A078600 A078601 KEYWORD nonn AUTHOR Aart Blokhuis (aartb(AT)win.tue.nl), Dec 09 2002 EXTENSIONS Corrected and extended by Michel Marcus, Apr 14 2013 Added more terms, Joerg Arndt, Apr 19 2013 STATUS approved

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Last modified August 8 19:29 EDT 2020. Contains 336298 sequences. (Running on oeis4.)