A352225 Second numbers F = a(n) of two non-consecutive numbers (E, F) different from (C, D) = (A352222(n), A352223(n)), 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.

-360, -197, -362, -2805, -3866, -10081, -29511, -5905, -227790, -10012, -24548, -28995, -875133, -73040, -615709, -457027, -3044074, -17549681, -4232837, -4999714, -13724102460, -94822721073

Offset

1,1

Comments

Numbers F 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 = A352223(n), E = A352224(n) and F = a(n) (this sequence).

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

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

A352224(n)^3 + a(n)^3 = A352221(n)^3 + (A352221(n) + 1)^3 = A352222(n)^3 + A352223(n)^3 = A352220(n).

Example

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

Crossrefs

Cf. A005898, A001235, A272885, A352133, A352134, A352135, A352136, A352220, A352221, A352222, A352223, A352224.

Sequence in context: A360943 A097570 A185641 * A031966 A137487 A069478

Adjacent sequences: A352222 A352223 A352224 * A352226 A352227 A352228

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