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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.

%I A352221 #31 Feb 16 2025 08:34:03
%S A352221 121,163,235,562,1090,1111,3280,5687,15187,15818,15934,24196,41674,
%T A352221 80062,167147,192629,292154,2778319,3532195,7906844,58400437,248878534
%N 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.
%C A352221 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).
%C A352221 Subsequence of A352134.
%H A352221 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 A352221 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredCubeNumber.html">Centered Cube Number</a>
%F A352221 a(n)^3 + (a(n)+1)^3 = A352222(n)^3 + A352223(n)^3 = A352224(n)^3 + A352225(n)^3 = A352220(n).
%e A352221 121 is a term because 121^3 + 122^3 = 153^3 + 18^3 = 369^3 + (-360)^3 = 3587409.
%Y A352221 Cf. A005898, A001235, A272885, A352133, A352134, A352135, A352136, A352220, A352222, A352223, A352224, A352225.
%K A352221 nonn,more
%O A352221 1,1
%A A352221 _Vladimir Pletser_, Mar 07 2022
%E A352221 a(6)-a(20) from _Jon E. Schoenfield_, Mar 10 2022
%E A352221 a(21) from _Chai Wah Wu_, Mar 17 2022
%E A352221 a(22) from _Bert Dobbelaere_, Apr 18 2022