cp's OEIS Frontend

A281224 Integer c such that (a^3 + b^3 - c^3)^2 = 1 where a,b,c are integers greater than 2.

%I A281224 #24 Dec 12 2021 22:35:13
%S A281224 9,12,103,144,150,172,249,495,505,577,729,738,904,1010,1210,1544,1852,
%T A281224 1988,2304,2316,3097,3753,4184,5262,5625,5640,6081,6756,8657,8703,
%U A281224 9791,9953,11664,11682,12884,14258,16849,18649,21279,21609,21630,24987,29737,31615
%N A281224 Integer c such that (a^3 + b^3 - c^3)^2 = 1 where a,b,c are integers greater than 2.
%C A281224 a^3 + b^3 = c^3 has no nontrivial integer solution, this list gives the "near misses" which satisfy a^3 + b^3 = c^3 +- 1.
%C A281224 If a (or b) = 1, then b (or a) = c will always satisfy a^3 + b^3 = c^3 + 1 (trivially).
%C A281224 If any of a,b,c is 0, the equation can be reduced to x^3 + y^3 = 1^3 (possibly taking negative values), which has no nontrivial solutions.
%H A281224 Chai Wah Wu, <a href="/A281224/b281224.txt">Table of n, a(n) for n = 1..200</a>
%e A281224     a    b    c
%e A281224   ---  ---  ---
%e A281224     6    8    9
%e A281224     9   10   12
%e A281224    64   94  103
%e A281224    71  138  144
%e A281224    73  144  150
%e A281224   135  138  172
%e A281224 E.g.: 135^3 + 138^3 = 172^3 - 1.
%t A281224 n = 500;
%t A281224 Do[If[a // IntegerQ,(*{a,b,c}*)c // Sow], {c, n}, {b, c/2^(1/3) // Ceiling, c - 1}, {a, ({-1, 1} + c^3 - b^3)^(1/3)}] // Reap // Last // Last(*//TableForm*)
%K A281224 nonn
%O A281224 1,1
%A A281224 _Albert Lau_, Jan 18 2017