In elementary number theory, a **centered square number** is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each centered square number equals the number of dots within a given city block distance of the center dot on a regular square lattice. While centered square numbers, like figurate numbers in general, have few if any direct practical applications, they are sometimes studied in recreational mathematics for their elegant geometric and arithmetic properties.

The figures for the first four centered square numbers are shown below:

center;">Read more about Centered Square Number: Relationships With Other Figurate Numbers, Properties

### Other articles related to "number, centered, centered square number, centered square, square numbers, centered square numbers, square, squares":

... 3003 – triangular

**number**, only

**number**known to appear eight times in Pascal's triangle no

**number**is known to appear more than eight times other than 1 ... Sophie Germain prime, 51st safe prime 3025 – 55 2, sum of the cubes of the first ten integers,

**centered**octagonal

**number**3045 – sum of the integers 196 to. 3249 – 57 2,

**centered**octagonal

**number**, member of a Ruth–Aaron pair with 3248 under second definition 3256 –

**centered**heptagonal

**number**3266 – sum of first 41 primes, 523rd ...

**Centered Square Number**- Properties - Centered Square Prime

... A

**centered square**prime is a

**centered square number**that is prime ... Unlike regular

**square numbers**, which are never prime, quite a few of the

**centered square numbers**are prime ... The first few

**centered square**primes are 5, 13, 41, 61, 113, 181, 313, 421, 613, 761, 1013, 1201, 1301, 1741, 1861, 2113, 2381, 2521, 3121, 3613, … (sequence A027862 in OEIS) ...

1501 –

**centered**pentagonal

**number**1511 – Sophie Germain prime, balanced prime 1513 –

**centered square number**1518 – Mertens function zero 1519 ... function for first 74 integers 1701 – decagonal

**number**, hull

**number**of the U.S.S ... Enterprise on Star Trek 1705 – tribonacci

**number**1709 – first of a sequence of eight primes formed by adding 57 in the middle ...

... these to obtain an octagonal prism with regular faces and two additional polyhedra called

**square**cupolae, which count among the Johnson solids it is thus an elongated

**square**... can be reassembled to give a new solid called the elongated

**square**gyrobicupola or pseudorhombicuboctahedron, with the symmetry of a

**square**antiprism ... of a rhombicuboctahedron, with one triangle and three

**squares**meeting at each, but are not all identical with respect to the entire polyhedron, since some are closer to the symmetry axis than others ...

... The K4 complete graph is often drawn as a square with all 6 edges connected ... This graph also represents an orthographic projection of the 4 vertices and 6 edges of the regular 3-simplex (tetrahedron) ...

### Famous quotes containing the words number, centered and/or square:

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