A295266 Positive integers whose squares can be represented as the sum or difference of 3-smooth numbers.

1, 2, 3, 5, 7, 17

Offset

1,2

Comments

In Chapter 7 of de Weger's tract, it is shown that there are no other terms.

More generally, de Weger exposited how one can determine all squares which can be represented as the sum or difference of k-smooth numbers for any given k and determined all integers whose squares can be represented as the sum or difference of 7-smooth numbers, among which the largest one is 14117^2 = 199289869 = 3^13 * 5^3 - 2 * 7^3.

Links

Table of n, a(n) for n=1..6.

B. M. M. de Weger, Algorithms for Diophantine Equations, Centrum voor Wiskunde en Informatica, Amsterdam, 1989.

Example

a(6) = 17 ; 17^2 = 288 + 1 = 2^5 * 3^2 + 1.

Crossrefs

Cf. A003586 (3-smooth numbers).

Coincides with A192579 and A215658 except the term 1.

Sequence in context: A343537 A192579 A215658 * A059471 A059496 A066814

Adjacent sequences: A295263 A295264 A295265 * A295267 A295268 A295269

Keyword

nonn,fini,full

Author

Tomohiro Yamada, Nov 19 2017

Status

approved