Difference between neighbor square and cube

[Hugo Pfoertner]

zak seidov wrote:
> 
> Max,
> thanks a lot for your (excellent as usual) reply!!
> 
> Using it I found:
> A054504(*
> Numbers n such that Mordell's equation y^2 = x^3 + n
> has no integral solutions. *)=
> {6, 7, 11, 13, 14, 20, 21, 23, 29, 32, 34, 39, 42, 45,
> 46, 47, 51, 53, 58, 59, 60, 61, 62, 66, 67, 69, 70,
> 74, 75, 77, 78, 83, 84, 85, 86, 87, 88, 90, 93, 95,
> 96, 102, 103, 104, 109, 110, 111, 114, 115, 116, 118,
> 123, 124, 130, 133, 135, 137, 139, 140, 146, 147, 149,
> 153, 155};
> 
> A081121=(*
> Numbers n such that Mordell's equation y^2 = x^3 - n
> has no integral solutions. *){
> 3, 5, 6, 9, 10, 12, 14, 16, 17, 21, 22, 24, 29, 30,
> 31, 32, 33, 34, 36, 37, 38, 41, 42, 43, 46, 50, 51,
> 52, 57, 58, 59, 62, 65, 66, 68, 69, 70, 73, 75, 77,
> 78, 80, 82, 84, 85, 86, 88, 90, 91, 92, 93, 94, 96,
> 97, 98, 99};
> 
> Intersection[A081121,A054504]
> ND={6,14,21,29,32,34,42,46,51,58,59,62,66,69,70,75,77,78,84,85,86,88,90,93,96}
> 
> And ND list gives
> (Absolute values of) Non-difference between square and
> cube (not only neighbor as in %C A125643).
> 
> Hence any number in ID should be in %C A125643.
> But 21 is in ND and absent in %C A125643!
> 
> Indeed in A125643,
> we have:
> ..,64,81,100,121,125,...,
> and 121-100=11^2-10^2=21!!
> 
> 21 is not difference between neighbor square and cube,
> but it is difference between neighbor terms in
> A125643.
> 
> As a result: my subject 'Difference between neighbor
> square and cube' is not correct,
> and in %C A125643 we have
> 'Difference between neighbor square/cube and
> square/cube'.
> 
> Sorry and thanks to Max & all seqfans,
> Zak

Also closely related:

http://www.research.att.com/~njas/sequences/A087285
http://www.research.att.com/~njas/sequences/A087286
http://www.research.att.com/~njas/sequences/A088017

Hugo