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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.
16
121, 163, 235, 562, 1090, 1111, 3280, 5687, 15187, 15818, 15934, 24196, 41674, 80062, 167147, 192629, 292154, 2778319, 3532195, 7906844, 58400437, 248878534
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
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.
KEYWORD
nonn,more
AUTHOR
Vladimir Pletser, Mar 07 2022
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
STATUS
approved