A352221 - OEIS

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

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OFFSET

1,1

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.

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

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

EXAMPLE

121 is a term because 121^3 + 122^3 = 153^3 + 18^3 = 369^3 + (-360)^3 = 3587409.

CROSSREFS