A180139 - OEIS

%I #5 Apr 14 2013 09:55:55

%S 4,6,33,36,38,64,66,137,569,5216,367807,939788,6369040,7885439,

%T 9536130,140292678,184151167,890838664,912903446,3171881613

%N a(n)=A179387(n)+1

%C Theorem (*Artur Jasinski*):

%C For any positive number x >= A180139(n) distance between cube of x and square of any y (such that x<>n^2 and y<>n^3) can't be less than A179386(n+1).

%C Proof: Because number of integral points of each Mordell elliptic curve of the form x^3-y^2 = k is finite and completely computable, such x can't exist.

%C If x=n^2 and y=n^3 distance d=0.

%C For d values see A179386.

%C For y values see A179388.

%e For numbers x from 4 to infinity distance can't be less than 4.

%e For numbers x from 6 to infinity distance can't be less than 7.

%e For numbers x from 33 to infinity distance can't be less than 26.

%e For numbers x from 36 to infinity distance can't be less than 28.

%e For numbers x from 38 to infinity distance can't be less than 49.

%e For numbers x from 66 to infinity distance can't be less than 60.

%e For numbers x from 137 to infinity distance can't be less than 63.

%e For numbers x from 569 to infinity distance can't be less than 174.

%e For numbers x from 5216 to infinity distance can't be less than 207.

%e For numbers x from 367807 to infinity distance can't be less than 307.

%Y Cf. A179107, A179108, A179109, A179387, A179388

%K hard,more,nonn

%O 1,1

%A _Artur Jasinski_, Aug 12 2010