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

1,1

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).

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

Formula

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

Example

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

Crossrefs

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

Sequence in context: A157891 A173644 A115991 * A143410 A114344 A350191

Adjacent sequences: A352133 A352134 A352135 * A352137 A352138 A352139

Keyword

sign

Author

Vladimir Pletser, Mar 05 2022

Status

approved