

A002648


A variant of the cuban primes: primes p = (x^3  y^3 )/(x  y) where x = y + 2.
(Formerly M4910 N2105)


7



13, 109, 193, 433, 769, 1201, 1453, 2029, 3469, 3889, 4801, 10093, 12289, 13873, 18253, 20173, 21169, 22189, 28813, 37633, 43201, 47629, 60493, 63949, 65713, 69313, 73009, 76801, 84673, 106033, 108301, 112909, 115249, 129793, 139969
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Primes p such that p = 1 + 3n^2 for some integer n.  Michael Somos, Sep 15 2005


REFERENCES

A. J. C. Cunningham, Binomial Factorisations, Vols. 19, Hodgson, London, 19231929; see Vol. 1, pp. 245259.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..5000
A. J. C. Cunningham, Binomial Factorisations, Vols. 19, Hodgson, London, 19231929. [Annotated scans of a few pages from Volumes 1 and 2]
Eric Weisstein's World of Mathematics, Cuban Prime
Wikipedia, Cuban prime


MATHEMATICA

Select[Table[3n^2+1, {n, 0, 700}], PrimeQ] (* Vincenzo Librandi, Dec 02 2011 *)


PROG

(PARI) {a(n)= local(m, c); if(n<1, 0, c=0; m=1; while( c<n, m++; if( isprime(m)&issquare((m1)/3), c++)); m)} /* Michael Somos, Sep 15 2005 */
(MAGMA) [a: n in [0..400]  IsPrime(a) where a is 3*n^2+1]; // Vincenzo Librandi, Dec 02 2011


CROSSREFS

Cf. A002407.
A subsequence of A007645.
Sequence in context: A084901 A006239 A142040 * A055840 A243417 A163845
Adjacent sequences: A002645 A002646 A002647 * A002649 A002650 A002651


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

Entry revised by N. J. A. Sloane, Jan 29 2013


STATUS

approved



