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A031363
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Positive numbers of form 5x^2-y^2; or, of form x^2+xy-y^2.
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4
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1, 4, 5, 9, 11, 16, 19, 20, 25, 29, 31, 36, 41, 44, 45, 49, 55, 59, 61, 64, 71, 76, 79, 80, 81, 89, 95, 99, 100, 101, 109, 116, 121, 124, 125, 131, 139, 144, 145, 149, 151, 155, 164, 169, 171, 176, 179, 180, 181, 191, 196, 199, 205, 209, 211, 220, 225, 229, 236
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Representable as x^2+3xy+y^2 with 0<=x<=y - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 16 2003
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REFERENCES
| M. Baake, "Solution of coincidence problem...", in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44.
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LINKS
| M. Baake and R. V. Moody, Similarity submodules and semigroups in Quasicrystals and Discrete Geometry, ed. J. Patera, Fields Institute Monographs, vol. 10 AMS, Providence, RI (1998) pp. 1-13.
J. H. Conway, E. M. Rains and N. J. A. Sloane, On the existence of similar sublattices, Canad. J. Math. 51 (1999), 1300-1306 (Abstract, pdf, ps).
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
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FORMULA
| Primes = 2 or 3 mod 5 occur with even exponents.
Nonzero terms in expansion of Dirichlet series Product_p (1-(Kronecker(m, p)+1)*p^(-s)+Kronecker(m, p)*p^(-2s))^(-1) for m= 5.
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MATHEMATICA
| ok[n_] := Resolve[ Exists[{x, y}, Element[x | y, Integers], n == 5*x^2 - y^2]]; Select[Range[236], ok] (* Jean-François Alcover Mar 21 2011 *)
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PROG
| (PARI) direuler(p=2, 101, 1/(1-(kronecker(5, p)*(X-X^2))-X))
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CROSSREFS
| See A035187 for number of representations.
Sequence in context: A117870 A162698 A166562 * A118142 A193584 A155149
Adjacent sequences: A031360 A031361 A031362 * A031364 A031365 A031366
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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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EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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