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

%I A230717 #33 Apr 22 2016 04:58:45
%S A230717 345744,1058841,1750329,8340544,22127616,67765824,68574961,95004009,
%T A230717 112021056,252047376,533794816,771895089,1097199376,1232922769,
%U A230717 1275989841,1416167424,2217373921,4337012736,4388797504,5402250000,5554571841,6080256576,7169347584,10721359936
%N A230717 Squares that are both a sum and a difference of two positive cubes.
%C A230717 Intersection of A050802 and A038596.
%C A230717 Square terms of sequence A225908. - _Michel Marcus_, Apr 22 2016
%D A230717 Ian Stewart, "Game, Set and Math", Dover, 2007, Chapter 8 'Close Encounters of the Fermat Kind', pp. 107-124.
%H A230717 Donovan Johnson and Chai Wah Wu, <a href="/A230717/b230717.txt">Table of n, a(n) for n = 1..500</a> n = 1..100 from Donovan Johnson
%H A230717 <a href="/index/Su#ssq">Index to sequences related to sums of cubes</a>
%F A230717 a(n) = k^2 = a^3 + b^3 = c^3 - d^3 for some natural numbers k, a, b, c, d.
%F A230717 a(n) = A230716(n)^2.
%e A230717 345744 = 588^2 = 14^3 + 70^3 = 71^3 - 23^3.
%o A230717 (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
%o A230717 isA050802(n)=for(k=sqrtnint((n+1)\2, 3), sqrtnint(n-1, 3), if(ispower(n-k^3, 3), return(issquare(n)))); 0
%o A230717 is(n)=isA038596(n) && isA050802(n) \\ _Charles R Greathouse IV_, Oct 28 2013
%Y A230717 Cf. A050801, A050802, A038596, A038597, A225908, A230716.
%K A230717 nonn
%O A230717 1,1
%A A230717 _Jonathan Sondow_, Oct 28 2013
%E A230717 a(5)-a(24) from _Donovan Johnson_, Oct 28 2013