This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A050792 #32 Feb 16 2025 08:32:40 %S A050792 9,64,73,135,334,244,368,1033,1010,577,3097,3753,1126,4083,5856,3987, %T A050792 1945,11161,13294,3088,10876,16617,4609,27238,5700,27784,11767,26914, %U A050792 38305,6562,49193,27835,35131,7364,65601,50313,9001,11980,39892,20848 %N A050792 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. %C A050792 "One of the simplest cubic Diophantine equations is known to have an infinite number of solutions (Lehmer, 1956; Payne and Vaserstein, 1991). Any number of solutions to the equation x^3 + y^3 + z^3 = 1 can be produced through the use of the algebraic identity (9t^3+1)^3 + (9t^4)^3 + (-9t^4-3t)^3 = 1 by substituting in values of t. ... %C A050792 "Although these are certainly solutions, the identity generates only one family of solutions. Other solutions such as (94, 64, -103), (235, 135, -249), (438, 334, -495), ... can be found. What is not known is if it is possible to parameterize all solutions for this equation. Put another way, are there an infinite number of families of solutions? Probable yes, but that too remains to be shown." [Herkommer] %C A050792 Values of x associated with A050794. %D A050792 Mark A. Herkommer, Number Theory, A Programmer's Guide, McGraw-Hill, NY, 1999, page 370. %D A050792 Ian Stewart, "Game, Set and Math", Chapter 8, 'Close Encounters of the Fermat Kind', Penguin Books, Ed. 1991, pp. 107-124. %H A050792 Lewis Mammel, <a href="/A050792/b050792.txt">Table of n, a(n) for n = 1..368</a> %H A050792 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DiophantineEquation3rdPowers.html">Diophantine Equation - 3rd Powers</a> %e A050792 577^3 + 2304^3 = 2316^3 + 1. %Y A050792 Cf. A050791, A050793, A050794. %K A050792 nonn %O A050792 1,1 %A A050792 _Patrick De Geest_, Sep 15 1999 %E A050792 More terms from _Michel ten Voorde_. %E A050792 Extended through 26914 by _Jud McCranie_, Dec 25 2000 %E A050792 More terms from _Don Reble_, Nov 29 2001 %E A050792 Edited by _N. J. A. Sloane_, May 08 2007