A050794 - OEIS

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

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OFFSET

1,1

COMMENTS

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

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.

EXAMPLE

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

CROSSREFS

Cf. A050791, A050792, A050793, A259753.

Sequence in context: A352970 A033502 A277366 * A138130 A306657 A048949

Adjacent sequences: A050791 A050792 A050793 * A050795 A050796 A050797

KEYWORD

nonn

AUTHOR

Patrick De Geest, Sep 15 1999

EXTENSIONS

Extended through 1594232306569 by Jud McCranie, Dec 25 2000

STATUS

approved