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 A001480 Let p = A007645(n) be the n-th generalized cuban prime and write p =  x^2 + 3*y^2; a(n) = y. (Formerly M0142 N0057) 12
 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, 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, 9, 6, 15, 5, 14, 16, 1, 3, 7, 10, 2, 5, 14, 17, 13, 9, 16, 17 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) = A000196((A007645(n) - A000290(A001479(n))) / 3). - Reinhard Zumkeller, Jul 11 2013 REFERENCES A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 1. 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). 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). LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 A. J. C. Cunningham, Quadratic Partitions, Hodgson, London, 1904 [Annotated scans of selected pages] S. R. Finch, Powers of Euler's q-Series, (arXiv:math.NT/0701251). B. van der Pol and P. Speziali, The primes in k(rho) (annotated and scanned copy) MATHEMATICA 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 *) PROG (Haskell) a001480 n = a000196 \$ (`div` 3) \$ (a007645 n) - (a001479 n) ^ 2 -- Reinhard Zumkeller, Jul 11 2013 (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 CROSSREFS Cf. A001479, A007645. Sequence in context: A318691 A075256 A334523 * A308117 A270755 A305030 Adjacent sequences:  A001477 A001478 A001479 * A001481 A001482 A001483 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Definition revised by N. J. A. Sloane, Jan 29 2013 STATUS approved

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Last modified May 16 22:04 EDT 2021. Contains 343955 sequences. (Running on oeis4.)