A230716 Numbers whose square is both a sum and a difference of two positive cubes.

588, 1029, 1323, 2888, 4704, 8232, 8281, 9747, 10584, 15876, 23104, 27783, 33124, 35113, 35721, 37632, 47089, 65856, 66248, 73500, 74529, 77976, 84672, 103544, 114075, 127008, 127896, 128625, 165375, 184832, 201684, 222264, 223587, 263169, 264992, 280904

Offset

1,1

Comments

Intersection of A050801 and A038597.

a(5)-a(24) are computed from Donovan Johnson's extension of A230717.

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)^2 = a^3 + b^3 = c^3 - d^3 for some natural numbers a, b, c, d.

a(n) = sqrt(A230717(n)).

Example

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

Crossrefs

Cf. A050801, A050802, A038596, A038597, A230717.

Sequence in context: A113509 A252387 A186395 * A211852 A178973 A259248

Adjacent sequences: A230713 A230714 A230715 * A230717 A230718 A230719

Keyword

nonn

Author

Jonathan Sondow, Oct 28 2013

Status

approved