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A295266 Positive integers whose squares can be represented as the sum or difference of 3-smooth numbers. 0
1, 2, 3, 5, 7, 17 (list; graph; refs; listen; history; text; internal format)



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.


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.


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


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




Tomohiro Yamada, Nov 19 2017



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Last modified December 4 04:49 EST 2021. Contains 349469 sequences. (Running on oeis4.)