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

1,1

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

Index to sequences related to sums of cubes

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

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

Sequence in context: A235429 A015321 A205420 * A350458 A254172 A254165

Adjacent sequences: A230714 A230715 A230716 * A230718 A230719 A230720

Keyword

nonn

Author

Jonathan Sondow, Oct 28 2013

Extensions

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

Status

approved