Properties
The first few centered square numbers are:
- 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221, 265, 313, 365, 421, 481, 545, 613, 685, 761, 841, 925, 1013, 1105, 1201, 1301, 1405, 1513, 1625, 1741, 1861, 1985, 2113, 2245, 2381, 2521, 2665, 2813, 2965, 3121, 3281, 3445, 3613, 3785, 3961, 4141, 4325, … (sequence A001844 in OEIS).
All centered square numbers are odd, and in base 10 one can notice the one's digits follows the pattern 1-5-3-5-1.
All centered square numbers and their divisors have a remainder of one when divided by four. Hence all centered square numbers and their divisors end with digits 1 or 5 in base 6, 8 or 12.
All centered square numbers except 1 are the third term of a Leg-Hypotenuse Pythagorean triple (for example, 3-4-5, 5-12-13).
Read more about this topic: Centered Square Number
Famous quotes containing the word properties:
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)