A352223 Second members D of two non-consecutive numbers such that the sums of their cubes are equal to centered cube numbers and to at least one other sum of two cubes, i.e., A = B^3 + (B+1)^3 = C^3 + D^3 = E^3 + F^3.

18, -5, 107, -125, 712, -1152, -1719, -865, -5370, -7870, 2518, -963, -29949, -20030, 111491, 87797, 261536, 2274319, -140357, -3938794, -139674130, -792131385

Offset

1,1

Comments

Numbers D such that A = B^3 + (B+1)^3 = C^3 + D^3 = E^3 + F^3 with C <> (D +- 1), E <> (F +- 1), E > C > B, C > |D| and E > |F|, where A = A352220(n), B = A352221(n), C = A352222(n), D = a(n) (this sequence), E = A352224(n) and F = A352225(n).

Terms in Data are ordered according to increasing order of A352220(n) or A352221(n).

Subsequence of A352136.

Links

Table of n, a(n) for n=1..22.

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

A352223(n)^3 + a(n)^3 = A352221(n)^3 + (A352221(n) + 1)^3 = A352224(n)^3 + A352225(n)^3 = A352220(n).

Example

18 belongs to the sequence as 153^3 + 18^3 = 121^3 + 122^3 = 369^3 + (-360)^3 = 3587409.

Crossrefs

Cf. A005898, A001235, A272885, A352133, A352134, A352135, A352136, A352220, A352221, A352222, A352224, A352225.

Sequence in context: A040312 A214893 A065909 * A186158 A331932 A038642

Adjacent sequences: A352220 A352221 A352222 * A352224 A352225 A352226

Keyword

sign,more

Author

Vladimir Pletser, Mar 07 2022

Extensions

a(21) from Chai Wah Wu, Mar 17 2022

a(22) from Bert Dobbelaere, Apr 18 2022

Status

approved