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%I M0166 N0065 #40 Feb 07 2017 11:39:54
%S 0,2,1,4,2,5,4,7,8,5,2,7,10,1,10,8,2,7,4,13,1,14,8,14,11,7,14,13,16,8,
%T 11,16,17,7,2,19,4,17,19,11,1,14,5,10,22,16,4,23,20,8,23,13,10,5,16,
%U 22,20,19,25,4,11,22,25,8,26,13,1,28,28,26,23,29,28
%N Let p = A007645(n) be the n-th generalized cuban prime and write p = x^2 + 3*y^2; a(n) = x.
%D A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 1.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D B. van der Pol and P. Speziali, The primes in k(rho). Nederl. Akad. Wetensch. Proc. Ser. A. {54} = Indagationes Math. 13, (1951). 9-15 (1 plate).
%H T. D. Noe, <a href="/A001479/b001479.txt">Table of n, a(n) for n = 1..1000</a>
%H A. J. C. Cunningham, <a href="/A002330/a002330.pdf">Quadratic Partitions</a>, Hodgson, London, 1904 [Annotated scans of selected pages]
%H S. R. Finch, <a href="http://arXiv.org/abs/math.NT/0701251">Powers of Euler's q-Series</a>, (arXiv:math.NT/0701251).
%H B. van der Pol and P. Speziali, <a href="/A001479/a001479.pdf">The primes in k(rho)</a> (annotated and scanned copy)
%t nmax = 56; nextCuban[p_] := If[p1 = NextPrime[p]; Mod[p1, 3] > 1, nextCuban[p1], p1]; cubanPrimes = NestList[ nextCuban, 3, nmax ]; f[p_] := x /. ToRules[ Reduce[x > 0 && y > 0 && p == x^2 + 3*y^2, {x, y}, Integers]]; a[1] = 0; a[n_] := f[cubanPrimes[[n]]]; Table[ a[n] , {n, 1, nmax}] (* _Jean-François Alcover_, Oct 19 2011 *)
%o (Haskell)
%o a001479 n = a000196 $ head $
%o filter ((== 1) . a010052) $ map (a007645 n -) $ tail a033428_list
%o -- _Reinhard Zumkeller_, Jul 11 2013
%o (PARI) do(lim)=my(v=List(), q=Qfb(1,0,3)); forprime(p=2,lim, if(p%3==2,next); listput(v, qfbsolve(q,p)[1])); Vec(v) \\ _Charles R Greathouse IV_, Feb 07 2017
%Y Cf. A001480, A007645, A000196, A010052, A033428.
%K nonn,easy,nice
%O 1,2
%A _N. J. A. Sloane_
%E Definition revised by _N. J. A. Sloane_, Jan 29 2013
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