A352224 First numbers E = 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.

369, 254, 419, 2820, 3923, 10090, 29538, 8310, 227835, 20739, 28391, 37494, 875196, 112295, 623814, 478788, 3045867, 17595980, 5473454, 10365237, 13724103165, 94822722216

Offset: 1

Author

Vladimir Pletser, Mar 07 2022

Keywords

• nonn
• more

Comments

Numbers E 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 = a(n) (this sequence) and F = A352225(n).

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

Examples

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

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

Crossrefs

Cf. A005898, A001235, A272885, A352133, A352134, A352135, A352136, A352220, A352221, A352222, A352223, A352225.

Formula

a(n)^3 + A352225(n)^3 = A352221(n)^3 + (A352221(n) + 1)^3 = A352222(n)^3 + A352223(n)^3 = A352220(n).

Extensions

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

a(22) from Bert Dobbelaere, Apr 18 2022