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%I #14 Apr 19 2013 12:13:46
%S 5,13,29,37,61,101,109,157,181,229,277,349,373,421,541,613,661,709,
%T 757,829,1021,1069,1093,1117,1213,1381,1429,1453,1549,1621,1669,1741,
%U 1789,1933,2029,2053,2221
%N 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.
%C 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.
%e 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)
%o (PARI) posipoly(pol) = {for (i=1, poldegree(pol), if (polcoeff(pol, i) <0, return(0));); return (1);}
%o 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
%K nonn
%O 1,1
%A Aart Blokhuis (aartb(AT)win.tue.nl), Dec 09 2002
%E Corrected and extended by _Michel Marcus_, Apr 14 2013
%E Added more terms, _Joerg Arndt_, Apr 19 2013
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