A352221 Numbers k such that the centered cube number k^3 + (k+1)^3 is equal to at least two other sums of two cubes.

121, 163, 235, 562, 1090, 1111, 3280, 5687, 15187, 15818, 15934, 24196, 41674, 80062, 167147, 192629, 292154, 2778319, 3532195, 7906844, 58400437, 248878534

Offset: 1

Author

Vladimir Pletser, Mar 07 2022

Keywords

• nonn
• more

Comments

Numbers B such that the centered cube number B^3 + (B+1)^3 is equal to at least two other sums of two cubes, i.e., 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 = a(n) (this sequence), C = A352222(n), D = A352223(n), E = A352224(n) and F = A352225(n).

Subsequence of A352134.

Examples

			121 is a term because 121^3 + 122^3 = 153^3 + 18^3 = 369^3 + (-360)^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, A352222, A352223, A352224, A352225.

Formula

a(n)^3 + (a(n)+1)^3 = A352222(n)^3 + A352223(n)^3 = A352224(n)^3 + A352225(n)^3 = A352220(n).

Extensions

a(6)-a(20) from Jon E. Schoenfield, Mar 10 2022

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

a(22) from Bert Dobbelaere, Apr 18 2022