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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.
18
-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
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.
KEYWORD
sign
AUTHOR
Vladimir Pletser, Mar 05 2022
STATUS
approved