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%I #37 Nov 30 2019 09:04:35
%S 1729,1092728,3375001,15438250,121287376,401947273,3680797185,
%T 6352182209,7856862273,12422690497,73244501505,145697644729,
%U 179406144001,648787169394,938601300672,985966166178,1594232306569
%N Consider the Diophantine equation x^3 + y^3 = z^3 + 1 (1 < x < y < z) or 'Fermat near misses'. Arrange solutions by increasing values of z (see A050791). Sequence gives values of x^3 + y^3 = z^3 + 1. For corresponding values of x, y, z see A050792, A050793, A050791 respectively.
%C Note that a(1)=1729 is the Hardy-Ramanujan number. - _Omar E. Pol_, Jan 28 2009
%D Ian Stewart, "Game, Set and Math", Chapter 8, 'Close Encounters of the Fermat Kind', Penguin Books, Ed. 1991, pp. 107-124.
%D David Wells, "Curious and Interesting Numbers", Revised Ed. 1997, Penguin Books, On number "1729", p. 153.
%H Uwe Hollerbach and David Rabahy, <a href="/A050794/b050794.txt">Table of n, a(n) for n = 1..368</a>[Terms 75 through 368 were computed by David Rabahy, Oct 13 2015]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DiophantineEquation3rdPowers.html">Diophantine Equation - 3rd Powers</a>
%e 577^3 + 2304^3 = 2316^3 + 1 = 12422690497.
%Y Cf. A050791, A050792, A050793, A259753.
%K nonn
%O 1,1
%A _Patrick De Geest_, Sep 15 1999
%E Extended through 1594232306569 by _Jud McCranie_, Dec 25 2000
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