A352135 Numbers j in pairs (j,k), with j <> k +- 1, such that the sum of their cubes is equal to a centered cube number.

6, 6, 12, 28, 41, 46, 151, 90, 171, 181, 153, 160, 206, 1016, 292, 378, 513, 531, 831, 633, 618, 3753, 710, 1119, 1410, 830, 1246, 1307, 1623, 1506, 1629, 1752, 1845, 1917, 1917, 2019, 10815, 2140, 22331, 2871, 3660, 4481, 3881, 4230, 43356, 9955, 6294, 76621, 22988, 7170, 21253

Offset

1,1

Comments

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).

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

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

Example

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

Crossrefs

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

Sequence in context: A315800 A160729 A315801 * A272349 A262850 A262849

Adjacent sequences: A352132 A352133 A352134 * A352136 A352137 A352138

Keyword

nonn

Author

Vladimir Pletser, Mar 05 2022

Extensions

Missing terms inserted by Jon E. Schoenfield, Mar 11 2022

Status

approved