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A001480
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Numbers y such that p = x^2 + 3y^2 for Cuban primes p = A007645(n)
(Formerly M0142 N0057)
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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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(p). Nederl. Akad. Wetensch. Proc. Ser. A. {54} = Indagationes Math. 13, (1951). 9-15 (1 plate).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
S. R. Finch, Powers of Euler's q-Series, (arXiv:math.NT/0701251).
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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}] (* From Jean-François Alcover, Oct 19 2011 *)
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CROSSREFS
| Cf. A001479.
Sequence in context: A060162 A026730 A075256 * A110917 A070956 A007828
Adjacent sequences: A001477 A001478 A001479 * A001481 A001482 A001483
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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