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.

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).

Links

Table of n, a(n) for n=1..50.

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

Adjacent sequences: A114362 A114363 A114364 * A114366 A114367 A114368

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