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A050787
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Consider the Diophantine equation x^3+y^3=z^3-1 (x<y<z) or 'Fermat near misses'. Arrange solutions by increasing values of z. Sequence gives values of z.
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6
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9, 144, 172, 505, 577, 729, 904, 1010, 1210, 2304, 3097, 3753, 5625, 6081, 6756, 8703, 11664, 12884, 16849, 18649, 21609, 24987, 29737, 36864, 37513, 38134, 38239, 41545, 49461, 51762, 59049, 66465, 68010, 69709, 71852, 73627, 78529
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| n^3-1 is expressible as the sum of two nonzero cubes.
The subsequence of primes in the sequence begins: 577, 38239, 69709. [From Jonathan Vos Post (jvospost3(AT)gmail.com), May 13 2010]
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REFERENCES
| Ian Stewart, "Game, Set and Math", Chapter 8, 'Close Encounters of the Fermat Kind', Penguin Books, Ed. 1991, pp. 107-124.
David Wells, "Curious and Interesting Numbers", Revised Ed. 1997, Penguin Books, On number "729", p. 147.
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LINKS
| Eric Weisstein's World of Mathematics, Diophantine Equation - 3rd Powers
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EXAMPLE
| 2304 is in the sequence because 575^3 + 2292^3 = 2304^3 - 1.
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MATHEMATICA
| r[z_] := Reduce[ 1 < x < y < z && x^3 + y^3 == z^3 - 1, {x, y}, Integers]; z = 4; A050787 = {}; While[z < 10^4, If[r[z] =!= False, Print[z]; AppendTo[A050787, z]]; z++]; A050787 (* From Jean-François Alcover, Dec 27 2011 *)
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CROSSREFS
| Cf. A050788, A050789, A050790, A050791.
Sequence in context: A137059 A083084 A187402 * A017198 A134176 A067415
Adjacent sequences: A050784 A050785 A050786 * A050788 A050789 A050790
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KEYWORD
| nonn,nice
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AUTHOR
| Patrick De Geest (pdg(AT)worldofnumbers.com), Sep 15 1999.
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EXTENSIONS
| More terms from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Dec 25 2000
More terms from Don Reble (djr(AT)nk.ca), Nov 29 2001
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