Template:Sequence of the Day for November 9

Intended for: November 9, 2012

Timetable

• First draft entered by Charles R Greathouse IV on July 29, 2011 ✓
• Draft to be reviewed by September 9, 2012
• Draft to be approved by October 9, 2012

Yesterday's SOTD * Tomorrow's SOTD

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A193018: The largest integer that cannot be written as the sum of squares of integers larger than

n, n   ≥   2

.

{ 23, 87, 119, 201, 312, 376, 455, 616, 760, 840, 1055, 1136, 1248, 1472, 1719, 1959, ... }

What is the true order of this sequence? Obviously, the smallest integer that can be written thusly is

(n + 1) 2

(or

2 (n + 1) 2

if we want two terms). The upper bound

a (n) < n 4 + 6 n 3 + 11 n 2 + 6 n

can be obtained via Sylvester’s theorem, so

n 2   ≪   a (n)   ≪   n 4

(the lower bound being trivial).