Search: id:A002407
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%I A002407 M4363 N1828
%S A002407 7,19,37,61,127,271,331,397,547,631,919,1657,1801,1951,2269,2437,2791,
%T A002407 3169,3571,4219,4447,5167,5419,6211,7057,7351,8269,9241,10267,11719,
%U A002407 12097,13267,13669,16651,19441,19927,22447,23497,24571,25117,26227
%N A002407 Cuban primes: primes of the form p = (x^3 - y^3 )/(x - y), x=y+1 (prime 
               hex numbers).
%C A002407 Primes equal to the difference of two consecutive cubes. - Lekraj Beedassy 
               (blekraj(AT)yahoo.com), Aug 21 2004
%C A002407 Primes p such that 4p = 1+3n^2 for some integer n. - Michael Somos Sep 
               15 2005
%C A002407 Equivalently, primes of the form p=1+3k(k+1) (and then k=floor(sqrt(p/
               3))). Also: primes p such that n^2(p+n) is a cube for some n>0. - 
               M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 28 2007
%C A002407 The cuban primes may be generated from the hexagonal centered numbers 
               by eliminating all the items that may be expressed as 36*i*j+6*i+6*j+1 
               with i,j integer [From Giacomo Fecondo (jackfertile(AT)alice.it), 
               Mar 13 2009, Mar 17 2009]
%D A002407 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002407 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002407 A. J. C. Cunningham, On quasi-Mersennian numbers, Mess. Math., 41 (1912), 
               119-146.
%D A002407 A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 
               1923-1929; see Vol. 1, pp. 245-259.
%D A002407 J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des 
               Nombres, Problem 241 pp. 39; 179, Ellipses Paris 2004.
%H A002407 T. D. Noe, <a href="b002407.txt">Table of n, a(n) for n=1..1000</a>
%H A002407 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CubanPrime.html">Cuban Prime</a>
%H A002407 Wikipedia, <a href="http://en.wikipedia.org/wiki/Cuban_prime">Cuban prime</
               a>
%e A002407 a(1) = 7 = 1+3k(k+1) with k=1 is the smallest prime of that form.
%e A002407 a(10^5) = 1792617147127 since this is the 100000th prime of that form.
%t A002407 lst={};Do[If[PrimeQ[p=(n+1)^3-n^3], (*Print[p];*)AppendTo[lst, p]], {n, 
               10^2}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 
               21 2008]
%o A002407 (PARI) {a(n)= local(m, c); if(n<1, 0, c=0; m=1; while( c<n, m++; if( 
               isprime(m)&issquare((4*m-1)/3), c++)); m)} /* Michael Somos Sep 15 
               2005 */
%o A002407 (PARI) A002407(n,k=1)=until(isprime(3*k*k+++1)&!n--,);3*k*k--+1 list_A2407(Nmax)=for(k=1,
               sqrt(Nmax/3),isprime(t=3*k*(k+1)+1)&print1(t",")) - M. F. Hasler 
               (Maximilian.Hasler(AT)gmail.com), Nov 28 2007
%Y A002407 Cf. A003215.
%Y A002407 Cf. A113478.
%Y A002407 Sequence in context: A113743 A003215 A133323 this_sequence A098484 A155443 
               A155405
%Y A002407 Adjacent sequences: A002404 A002405 A002406 this_sequence A002408 A002409 
               A002410
%K A002407 nonn,easy,nice
%O A002407 1,1
%A A002407 N. J. A. Sloane (njas(AT)research.att.com).
%E A002407 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 08 2000

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