A050794 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.

1729, 1092728, 3375001, 15438250, 121287376, 401947273, 3680797185, 6352182209, 7856862273, 12422690497, 73244501505, 145697644729, 179406144001, 648787169394, 938601300672, 985966166178, 1594232306569

Offset: 1

Author

Patrick De Geest, Sep 15 1999

Keywords

• nonn

Comments

Note that a(1)=1729 is the Hardy-Ramanujan number. - Omar E. Pol, Jan 28 2009

Examples

			577^3 + 2304^3 = 2316^3 + 1 = 12422690497.
		

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 "1729", p. 153.

Links

• Uwe Hollerbach and David Rabahy, Table of n, a(n) for n = 1..368, a(n) for n = 75..368 by David Rabahy, Oct 13 2015.
• Shyam Sunder Gupta, On Some Special Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 22, 527-565.
• Eric Weisstein's World of Mathematics, Diophantine Equation - 3rd Powers.

Crossrefs

Cf. A050791, A050792, A050793, A259753.

Extensions

Extended through 1594232306569 by Jud McCranie, Dec 25 2000