A001479 Let p = A007645(n) be the n-th generalized cuban prime and write p = x^2 + 3*y^2; a(n) = x. (Formerly M0166 N0065)

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, 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, 22, 20, 19, 25, 4, 11, 22, 25, 8, 26, 13, 1, 28, 28, 26, 23, 29, 28

Offset

1,2

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 = 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 *)

Prog

(Haskell)
a001479 n = a000196 $ head $
   filter ((== 1) . a010052) $ map (a007645 n -) $ tail a033428_list
-- 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)[1])); Vec(v) \\ Charles R Greathouse IV, Feb 07 2017

Crossrefs

Cf. A001480, A007645, A000196, A010052, A033428.

Sequence in context: A124896 A008742 A029136 * A128861 A161307 A161241

Adjacent sequences: A001476 A001477 A001478 * A001480 A001481 A001482

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

Definition revised by N. J. A. Sloane, Jan 29 2013

Status

approved