%I #42 Dec 31 2023 12:36:29

%S 6,6,12,28,41,46,151,90,171,181,153,160,206,1016,292,378,513,531,831,

%T 633,618,3753,710,1119,1410,830,1246,1307,1623,1506,1629,1752,1845,

%U 1917,1917,2019,10815,2140,22331,2871,3660,4481,3881,4230,43356,9955,6294,76621,22988,7170,21253

%N Numbers j in pairs (j,k), with j <> k +- 1, such that the sum of their cubes is equal to a centered cube number.

%C Numbers j such that j^3 + k^3 = m^3 + (m + 1)^3 = N, with j <> (k +- 1), j > m and j > |k|, and where j = a(n) (this sequence), k = A352136(n), m = A352134(n) and N = A352133(n).

%C In case there are two or more pairs of numbers (j, k) such that the sum of their cubes equals the same centered cube number, the smallest occurrence of j is shown in the sequence. For other occurrences, see A352224(n) and A352225(n).

%C Terms in Data are ordered according to increasing order of A352133(n) or A352134(n).

%H Vladimir Pletser, <a href="/A352135/b352135.txt">Table of n, a(n) for n = 1..258</a>

%H A. Grinstein, <a href="https://web.archive.org/web/20040320144821/http://zadok.org/mattandloraine/1729.html">Ramanujan and 1729</a>, University of Melbourne Dept. of Math and Statistics Newsletter: Issue 3, 1998.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredCubeNumber.html">Centered Cube Number</a>

%F a(n)^3 + A352136(n)^3 = A352134(n)^3 + (A352134(n) + 1)^3 = A352133(n).

%e 6 belongs to the sequence as 6^3 + (-5)^3 = 3^3 + 4^3 = 91.

%Y Cf. A005898, A001235, A272885, A352133, A352134, A352136, A352220, A352221, A352222, A352223, A352224, A352225.

%K nonn

%O 1,1

%A _Vladimir Pletser_, Mar 05 2022

%E Missing terms inserted by _Jon E. Schoenfield_, Mar 11 2022