A352136 Numbers k in pairs (j,k), with j <> k +- 1, such that the sum of their cubes is equal to a centered cube number.

-5, -3, 1, -21, -6, -3, -148, -69, -136, -150, 18, -69, -5, -1011, 107, 93, -236, -218, -740, -312, -21, -3746, -125, -984, -1319, -359, -963, 712, -1152, -815, 178, -569, -706, -382, 346, -982, -10794, -69, -22320, -1866, -2831, -3246, 1614, -1719, -43343, -9456, -197, -76606, -22757, -865, -20976

Offset: 1

Author

Vladimir Pletser, Mar 05 2022

Keywords

• sign

Comments

Numbers k such that j^3 +k^3 = m^3 + (m + 1)^3 = N, with j <> (k +- 1), j > m and j > |k|, and where j = A352135(n), k = a(n) (this sequence), m = A352134(n) and N = A352133(n).

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).

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

Examples

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

Links

• Vladimir Pletser, Table of n, a(n) for n = 1..258
• A. Grinstein, Ramanujan and 1729, University of Melbourne Dept. of Math and Statistics Newsletter: Issue 3, 1998.
• Eric Weisstein's World of Mathematics, Centered Cube Number

Crossrefs

Cf. A005898, A001235, A272885, A352133, A352134, A352135, A352220, A352221, A352222, A352223, A352224, A352225.

Formula

A352135(n)^3 + a(n)^3 = A352134(n)^3 + (A352134(n) + 1)^3 = A352133(n).