A188620 Primes of the form x^3 + y^3 + 1.

3, 17, 29, 73, 127, 251, 281, 433, 521, 577, 757, 1009, 1217, 1459, 2663, 2729, 2753, 2927, 3257, 3457, 3529, 3719, 5039, 5573, 5897, 6833, 6841, 7561, 7589, 8009, 8191, 8513, 9001, 9929, 10657, 11161, 12097, 12377, 12511, 12637, 13499, 16001, 16481, 17921, 18089, 18523, 19001

Offset

1,1

Comments

x+y+1 also is a prime in most small cases.

As a(n) becomes large, it appears that x+y+1 is usually not prime; this is what one would expect. - Franklin T. Adams-Watters Apr 05 2011

Links

Table of n, a(n) for n=1..47.

Example

757 belongs to the sequence because 757 = 9^3+3^3+1 = 729+27+1.

Mathematica

nn = 20000; lim = Floor[nn^(1/3)]; Union[Reap[Do[p = a^3 + b^3 + 1; If[p <= nn && PrimeQ[p], Sow[p]], {a, lim}, {b, a}]][[2, 1]]] (* T. D. Noe, Apr 06 2011 *)

Crossrefs

Sequence in context: A063715 A105411 A107158 * A152529 A126782 A090648

Adjacent sequences: A188617 A188618 A188619 * A188621 A188622 A188623

Keyword

nonn

Author

Carmine Suriano, Apr 05 2011

Extensions

Corrected by T. D. Noe, Apr 06 2011

Status

approved