A230717 Squares that are both a sum and a difference of two positive cubes.

345744, 1058841, 1750329, 8340544, 22127616, 67765824, 68574961, 95004009, 112021056, 252047376, 533794816, 771895089, 1097199376, 1232922769, 1275989841, 1416167424, 2217373921, 4337012736, 4388797504, 5402250000, 5554571841, 6080256576, 7169347584, 10721359936

Offset: 1

Author

Jonathan Sondow, Oct 28 2013

Keywords

• nonn

Comments

Intersection of A050802 and A038596.

Square terms of sequence A225908. - Michel Marcus, Apr 22 2016

Examples

			345744 = 588^2 = 14^3 + 70^3 = 71^3 - 23^3.
		

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
• Index to sequences related to sums of cubes

Crossrefs

Cf. A050801, A050802, A038596, A038597, A225908, A230716.

Programs

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

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.

Extensions

a(5)-a(24) from Donovan Johnson, Oct 28 2013