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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
Intersection of A050802 and A038596.
Square terms of sequence A225908. - Michel Marcus, Apr 22 2016
REFERENCES
Ian Stewart, "Game, Set and Math", Dover, 2007, Chapter 8 'Close Encounters of the Fermat Kind', pp. 107-124.
LINKS
Donovan Johnson and Chai Wah Wu, Table of n, a(n) for n = 1..500 n = 1..100 from Donovan Johnson
FORMULA
a(n) = k^2 = a^3 + b^3 = c^3 - d^3 for some natural numbers k, a, b, c, d.
a(n) = A230716(n)^2.
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
is(n)=isA038596(n) && isA050802(n) \\ Charles R Greathouse IV, Oct 28 2013
CROSSREFS
Sequence in context: A235429 A015321 A205420 * A350458 A254172 A254165
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Oct 28 2013
EXTENSIONS
a(5)-a(24) from Donovan Johnson, Oct 28 2013
STATUS
approved

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)