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%I M0142 N0057 #36 Feb 07 2017 11:40:27
%S 1,1,2,1,3,2,3,2,1,4,5,4,1,6,3,5,7,6,7,2,8,1,7,3,6,8,5,6,3,9,8,5,4,10,
%T 11,2,11,6,4,10,12,9,12,11,1,9,13,2,7,13,4,12,13,14,11,7,9,10,4,15,14,
%U 9,6,15,5,14,16,1,3,7,10,2,5,14,17,13,9,16,17
%N Let p = A007645(n) be the n-th generalized cuban prime and write p = x^2 + 3*y^2; a(n) = y.
%C a(n) = A000196((A007645(n) - A000290(A001479(n))) / 3). - _Reinhard Zumkeller_, Jul 11 2013
%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="/A001480/b001480.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 = 63; nextCuban[p_] := If[p1 = NextPrime[p]; Mod[p1, 3] > 1, nextCuban[p1], p1]; cubanPrimes = NestList[ nextCuban, 3, nmax ]; f[p_] := y /. ToRules[ Reduce[x > 0 && y > 0 && p == x^2 + 3*y^2, {x, y}, Integers]]; a[1] = 1; a[n_] := f[cubanPrimes[[n]]]; Table[ a[n] , {n, 1, nmax}] (* _Jean-François Alcover_, Oct 19 2011 *)
%o (Haskell)
%o a001480 n = a000196 $ (`div` 3) $ (a007645 n) - (a001479 n) ^ 2
%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)[2])); Vec(v) \\ _Charles R Greathouse IV_, Feb 07 2017
%Y Cf. A001479, A007645.
%K nonn,easy,nice
%O 1,3
%A _N. J. A. Sloane_
%E Definition revised by _N. J. A. Sloane_, Jan 29 2013
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