Template:Sequence of the Day for June 27

Intended for: June 27, 2013

Timetable

• First draft entered by Alonso del Arte on November 8, 2012 ✓
• Draft reviewed by April 27, 2013
• Draft approved by May 27, 2013

Yesterday's SOTD * Tomorrow's SOTD

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A002378: Pronic numbers

n 2  +  n

.

{0, 2, 6, 12, ..., 1722, 1806, 1892, 1980, 2070, 2162, 2256, ...}

The mathematician Augustus De Morgan was born on this date in 1806. When he turned 43 in 1849, he noticed that his age happened to be the square root of the year. The reason this was the case is that the year of his birth is a pronic number. These are numbers of the form

n 2  +  n

, but they can also be expressed as

n 2  −  n

(with a different offset, of course). Thus 1849 = 43 2, and 1806 = 43 2 – 43. People born in 1892 may have noticed a similar situation applied when they turned 44, but among those who are still with us today, people born in 1980 who are still alive in 2025 will then be able to say that their age is the square root of the year.