OFFSET
1,1
COMMENTS
Solutions x to the equations x = a^3 + b^3 = c^3 - d^3 in positive integers.
The intersection of A003325 and A181123. See those sequences for additional comments, references, links and cross-refs.
REFERENCES
Shiraishi Chochu (aka Shiraishi Nagatada), Shamei Sampu (Sacred Mathematics), 1826.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
David Eugene Smith and Yoshio Mikami, A History of Japanese Mathematics, Open Court, Chicago, 1914; Dover reprint, 2004; pp. 233-235.
Wikipedia (French), Shiraishi Nagatada
Wikipedia (German), Shiraishi Nagatada
EXAMPLE
3^3 + 4^3 + 5^3 = 6^3, so 3^3 + 4^3 = 91 and 3^3 + 5^3 = 152 and 4^3 + 5^3 = 189 are members.
MATHEMATICA
nn = 3*10^4; t1 = Union[Flatten[Table[x^3 + y^3, {x, nn^(1/3)}, {y, x, (nn - x^3)^(1/3)}]]]; p = 3; t2 = Union[Reap[Do[n = i^p - j^p; If[n <= nn, Sow[n]], {i, Ceiling[(nn/p)^(1/(p - 1))]}, {j, i}]][[2, 1]]]; Intersection[t1, t2] (* T. D. Noe, Jun 21 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Jun 21 2013
STATUS
approved