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A180139 a(n)=A179387(n)+1 1
4, 6, 33, 36, 38, 64, 66, 137, 569, 5216, 367807, 939788, 6369040, 7885439, 9536130, 140292678, 184151167, 890838664, 912903446, 3171881613 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Theorem (*Artur Jasinski*):

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).

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.

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

For d values see A179386.

For y values see A179388.

LINKS

Table of n, a(n) for n=1..20.

EXAMPLE

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

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

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

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

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

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

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

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

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

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

CROSSREFS

Cf. A179107, A179108, A179109, A179387, A179388

Sequence in context: A229712 A331513 A164127 * A222490 A071394 A137021

Adjacent sequences:  A180136 A180137 A180138 * A180140 A180141 A180142

KEYWORD

hard,more,nonn

AUTHOR

Artur Jasinski, Aug 12 2010

STATUS

approved

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Last modified November 27 16:20 EST 2021. Contains 349394 sequences. (Running on oeis4.)