A352225 - OEIS

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.

%I #34 Apr 18 2022 10:15:31

%S -360,-197,-362,-2805,-3866,-10081,-29511,-5905,-227790,-10012,-24548,

%T -28995,-875133,-73040,-615709,-457027,-3044074,-17549681,-4232837,

%U -4999714,-13724102460,-94822721073

%N 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.

%C 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).

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

%H A. Grinstein, <a href="https://web.archive.org/web/20040320144821/http://zadok.org/mattandloraine/1729.html">Ramanujan and 1729</a>, University of Melbourne Dept. of Math and Statistics Newsletter: Issue 3, 1998.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CenteredCubeNumber.html">Centered Cube Number</a>

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

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

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

%K sign,more

%O 1,1

%A _Vladimir Pletser_, Mar 07 2022

%E a(21) from _Chai Wah Wu_, Mar 17 2022

%E a(22) from _Bert Dobbelaere_, Apr 18 2022