Template:Sequence of the Day for April 14

Intended for: April 14, 2013

Timetable

• First draft entered by Alonso del Arte on March 17, 2012 ✓
• Draft reviewed by Daniel Forgues on April 13, 2016 ✓
• Draft to be approved by March 14, 2013

Yesterday's SOTD * Tomorrow's SOTD

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A003325: Numbers that are the sum of 2 positive cubes.

{ 2, 9, 16, 28, 35, 54, 65, 72, ... }

The positive cubes are not necessarily distinct (hence some terms are of the form

2 n 3

). Here it is necessary to specify "positive cubes" where it was not necessary with numbers that are the sum of 2 squares (since obviously

n 2 ∈ ℤ +

as long as

n   ≠   0

). With cubes we could very well have

37 = 4 3 + ( − 3) 3

, to give just one example. A conjecture that still stands is that this sequence and the sequence of numbers of the form

n 3 ± 3

have infinitely many terms in common, yet the only known example is

4 3 + 4 3 = 5 3 + 3 = 128

.