A352222 First members C of two non-consecutive numbers 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.

153, 206, 292, 710, 1307, 1623, 4230, 7170, 19275, 20331, 20063, 30486, 55572, 101135, 199614, 238806, 317427, 3145700, 4450334, 10163157, 146173525, 808182534

Offset

1,1

Comments

Numbers C 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 = a(n) (this sequence), D = A352223(n), E = A352224(n) and F = A352225(n).

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

Subsequence of A352135.

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 + A352223(n)^3 = A352221(n)^3 + (A352221(n) + 1)^3 = A352224(n)^3 + A352225(n)^3 = A352220(n).

Example

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

Crossrefs

Cf. A005898, A001235, A272885, A352133, A352134, A352135, A352136, A352220, A352221, A352223, A352224, A352225.

Sequence in context: A203603 A272767 A104810 * A253023 A194660 A348938

Adjacent sequences: A352219 A352220 A352221 * A352223 A352224 A352225

Keyword

nonn,more

Author

Vladimir Pletser, Mar 07 2022

Extensions

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

a(22) from Bert Dobbelaere, Apr 18 2022

Status

approved