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

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

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)

Crossrefs

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

Programs

Haskell

a001479 n = a000196 $ head $
   filter ((== 1) . a010052) $ map (a007645 n -) $ tail a033428_list
-- Reinhard Zumkeller, Jul 11 2013

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 *)

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

Extensions

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