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%I #7 Oct 01 2013 17:58:23
%S 3,19,5,7,389,59,67,11,83,13,773,107,7177,17,131,19,2381,163,23,179,
%T 23011,98321,5407,211,29,227,31,30011,251,2053,57037,7351,37,2309,
%U 63949,307,41,8647,43,2693,347,9511,47,23561,379,1327,25609,53,419,564367
%N Start with the empty list; for k = 1..oo, append to the list the smallest prime of the form k*m^3+m+1 with m>0 if such a prime exists, otherwise skip this value of k.
%C There are no primes in the sequence for k = 4,18,48,...,n(n+1)^2. This is because n(n+1)^2x^3 + x + 1 = ((n+1)x+1)((n^2 + n)x^2 - nx + 1).
%o (PARI) g2(n,p) = for(k=1,n,for(x=1,n,y=k*x^3+x+p;if(isprime(y),print1(y",");break)))
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Feb 09 2006
%E Better definition from _Omar E. Pol_, Aug 06 2009, Aug 08 2009.
%E Edited by _N. J. A. Sloane_, Aug 11 2009
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