Template:Sequence of the Day for July 16

Intended for: July 16, 2012

Timetable

First draft entered by Alonso del Arte on July 10, 2011 ✓
Draft reviewed by Alonso del Arte on May 10, 2012 ✓, Daniel Forgues on Jul 16, 2018 ✓
Draft to be approved by June 16, 2012

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A004215: Numbers that are the sum of 4 but no fewer nonzero squares. (Numbers of the form

4 i (8 j + 7), i ≥ 0, j ≥ 0

. [A.-M. Legendre & C. F. Gauss])

{ 7, 15, 23, 28, 31, 39, 47, ... }

From Waring’s problem we know that all positive integers can be expressed as a sum of at most four squares. In fact, most numbers can be expressed as the sum of fewer than four squares, even though the perfect squares thin out quadratically.