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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-Fran├žois 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: A060162 A026730 A075256 * A270755 A110917 A070956

Adjacent sequences:  A001477 A001478 A001479 * A001481 A001482 A001483

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved

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Last modified February 24 13:14 EST 2018. Contains 299623 sequences. (Running on oeis4.)