cp's OEIS Frontend

A352224 First numbers E = a(n) of two non-consecutive numbers (E, F) different from (C, D) = (A352222(n), A352223(n)), 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.

%I A352224 #37 Feb 16 2025 08:34:03
%S A352224 369,254,419,2820,3923,10090,29538,8310,227835,20739,28391,37494,
%T A352224 875196,112295,623814,478788,3045867,17595980,5473454,10365237,
%U A352224 13724103165,94822722216
%N A352224 First numbers E = a(n) of two non-consecutive numbers (E, F) different from (C, D) = (A352222(n), A352223(n)), 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.
%C A352224 Numbers E 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 = A352222(n), D = A352223(n), E = a(n) (this sequence) and F = A352225(n).
%C A352224 Terms are ordered according to increasing order of A352220(n) or A352221(n).
%H A352224 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 A352224 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredCubeNumber.html">Centered Cube Number</a>
%F A352224 a(n)^3 + A352225(n)^3 = A352221(n)^3 + (A352221(n) + 1)^3 = A352222(n)^3 + A352223(n)^3 = A352220(n).
%e A352224 369 belongs to the sequence as 369^3 + (-360)^3 = 121^3 + 122^3 = 153^3 + 18^3 = 3587409.
%Y A352224 Cf. A005898, A001235, A272885, A352133, A352134, A352135, A352136, A352220, A352221, A352222, A352223, A352225.
%K A352224 nonn,more
%O A352224 1,1
%A A352224 _Vladimir Pletser_, Mar 07 2022
%E A352224 a(21) from _Chai Wah Wu_, Mar 17 2022
%E A352224 a(22) from _Bert Dobbelaere_, Apr 18 2022