|
|
A230717
|
|
Squares that are both a sum and a difference of two positive cubes.
|
|
2
|
|
|
345744, 1058841, 1750329, 8340544, 22127616, 67765824, 68574961, 95004009, 112021056, 252047376, 533794816, 771895089, 1097199376, 1232922769, 1275989841, 1416167424, 2217373921, 4337012736, 4388797504, 5402250000, 5554571841, 6080256576, 7169347584, 10721359936
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
REFERENCES
|
Ian Stewart, "Game, Set and Math", Dover, 2007, Chapter 8 'Close Encounters of the Fermat Kind', pp. 107-124.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = k^2 = a^3 + b^3 = c^3 - d^3 for some natural numbers k, a, b, c, d.
|
|
EXAMPLE
|
345744 = 588^2 = 14^3 + 70^3 = 71^3 - 23^3.
|
|
PROG
|
(PARI) isA038596(n)=for(k=sqrtnint(n, 3)+1, (sqrtint(12*n-3)+3)\6, if(ispower(n-k^3, 3), return(issquare(n)))); 0
isA050802(n)=for(k=sqrtnint((n+1)\2, 3), sqrtnint(n-1, 3), if(ispower(n-k^3, 3), return(issquare(n)))); 0
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|