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A002648
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A variant of the cuban primes: primes p = (x^3 - y^3 )/(x - y) where x=y+2.
(Formerly M4910 N2105)
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6
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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
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OFFSET
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1,1
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COMMENTS
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Primes p such that p = 1+3n^2 for some integer n. - Michael Somos Sep 15 2005
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REFERENCES
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A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929; see Vol. 1, pp. 245-259.
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).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..5000
Eric Weisstein's World of Mathematics, Cuban Prime
Wikipedia, Cuban prime
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MATHEMATICA
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Select[Table[3n^2+1, {n, 0, 700}], PrimeQ] (* Vincenzo Librandi, Dec 02 2011 *)
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PROG
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(PARI) {a(n)= local(m, c); if(n<1, 0, c=0; m=1; while( c<n, m++; if( isprime(m)&issquare((m-1)/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
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CROSSREFS
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Cf. A002407.
A subsequence of A007645.
Sequence in context: A084901 A006239 A142040 * A055840 A163845 A075143
Adjacent sequences: A002645 A002646 A002647 * A002649 A002650 A002651
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Entry revised by N. J. A. Sloane, Jan 29 2013
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STATUS
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approved
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