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A114365
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.
0
3, 19, 5, 7, 389, 59, 67, 11, 83, 13, 773, 107, 7177, 17, 131, 19, 2381, 163, 23, 179, 23011, 98321, 5407, 211, 29, 227, 31, 30011, 251, 2053, 57037, 7351, 37, 2309, 63949, 307, 41, 8647, 43, 2693, 347, 9511, 47, 23561, 379, 1327, 25609, 53, 419, 564367
OFFSET
1,1
COMMENTS
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).
PROG
(PARI) g2(n, p) = for(k=1, n, for(x=1, n, y=k*x^3+x+p; if(isprime(y), print1(y", "); break)))
CROSSREFS
Sequence in context: A258200 A258007 A293700 * A084559 A272815 A179767
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Feb 09 2006
EXTENSIONS
Better definition from Omar E. Pol, Aug 06 2009, Aug 08 2009.
Edited by N. J. A. Sloane, Aug 11 2009
STATUS
approved