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A050791
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Consider the Diophantine equation x^3+y^3=z^3+1 (1<x<y<z) or 'Fermat near misses'. Sequence gives values of z in monotonic increasing order.
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11
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12, 103, 150, 249, 495, 738, 1544, 1852, 1988, 2316, 4184, 5262, 5640, 8657, 9791, 9953, 11682, 14258, 21279, 21630, 31615, 36620, 36888, 38599, 38823, 40362, 41485, 47584, 57978, 59076, 63086, 73967, 79273, 83711, 83802, 86166, 90030
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Numbers n such that n^3+1 is expressible as the sum of two nonzero cubes (both greater than 1).
Values of z associated with A050794.
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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.
Mohammad K. Azarian, Diophantine Pair, Problem B-881, Fibonacci Quarterly, Vol. 37, No. 3, August 1999, pp. 277-278. Solution appeared in Vol. 38, No. 2, May 2000, pp. 183-184.
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LINKS
| Lewis Mammel, Table of n, a(n) for n = 1..368
S. Ramanujan, Question 681, J. Ind. Math. Soc.
Eric Weisstein's World of Mathematics, Diophantine Equation - 3rd Powers
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EXAMPLE
| 2316 is in the sequence because 577^3 + 2304^3 = 2316^3 + 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; A050791 = {}; While[z < 10^4, If[r[z] =!= False, Print[z]; AppendTo[A050791, z]]; z++]; A050791 (* From Jean-François Alcover, Dec 27 2011 *)
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CROSSREFS
| Cf. A050792, A050793, A050794, A050787.
Sequence in context: A052148 A133384 A052067 * A005771 A016228 A016276
Adjacent sequences: A050788 A050789 A050790 * A050792 A050793 A050794
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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 Michel ten Voorde (seqfan(AT)tenvoorde.org)
Extended through 47584 by Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Dec 25 2000
More terms from Don Reble (djr(AT)nk.ca), Nov 29 2001
Edited by N. J. A. Sloane (njas(AT)research.att.com), May 08 2007
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