147 (number)

← 146 147 148 →
← 140 141 142 143 144 145 146 147 148 149 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred forty-seven
Ordinal	147th (one hundred forty-seventh)
Factorization	3 × 72
Divisors	1, 3, 7, 21, 49, 147
Greek numeral	ΡΜΖ´
Roman numeral	CXLVII
Binary	100100112
Ternary	121103
Senary	4036
Octal	2238
Duodecimal	10312
Hexadecimal	9316

147 (one hundred [and] forty-seven) is the natural number following 146 and preceding 148.

In mathematics

147 is the fourth centered icosahedral number. These are a class of figurate numbers that represent points in the shape of a regular icosahedron or alternatively points in the shape of a cuboctahedron, and are magic numbers for the face-centered cubic lattice. ^[1] Separately, it is also a magic number for the diamond cubic. ^[2]

It is also the fourth Apéry number ${\displaystyle a_{3}}$ following 19, where ^[3]

$${\displaystyle a_{n}=\sum _{k=0}^{n}{\binom {n}{k}}^{2}{\binom {n+k}{k}},}$$

with 147 the composite index of the nineteenth triangle number, 190. ^{[4] [5]}

There are 147 different ways of representing one as a sum of unit fractions with five terms, allowing repeated fractions, ^[6] and 147 different self-avoiding polygonal chains of length six using horizontal and vertical segments of the integer lattice. ^[7]

In other fields

147 is the highest possible break in snooker, in the absence of fouls and refereeing errors. ^[8]

In some traditions, there are 147 psalms. However, current Christian and Jewish traditions list a larger number, leading to the suggestion that some of the psalms in the earlier numbering were split into multiple pieces. ^{[9] [10]}

147 is the telephonic number of the 27 Brazilian Civil Police forces.

See also

• 147 (disambiguation)

References

1. Sloane, N. J. A. (ed.). "SequenceA005902(Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA007904(Crystal ball sequence for diamond)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Sloane, N. J. A. (ed.). "SequenceA005258(Apéry numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
4. Sloane, N. J. A. (ed.). "SequenceA002808(The composite numbers: numbers n of the form x*y for x > 1 and y > 1.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-12-29.
5. Sloane, N. J. A. (ed.). "SequenceA000217(Triangular number: a(n) is the binomial(n+1,2) equivalent to n*(n+1)/2 that is 0 + 1 + 2 + ... + n.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-12-29.
6. Sloane, N. J. A. (ed.). "SequenceA002966(Egyptian fractions: number of solutions of 1 = 1/x_1 + ... + 1/x_n where 0 < x_1 ≤ ... ≤ x_n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
7. Sloane, N. J. A. (ed.). "SequenceA037245(Number of unrooted self-avoiding walks of n steps on square lattice)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
8. Hill, Andrew P.; Mallinson-Howard, Sarah H.; Madigan, Daniel J.; Jowett, Gareth E. (2020). "Perfectionism in Sport, Dance, and Exercise". In Tenenbaum, Gershon; Eklund, Robert C. (eds.). Handbook of Sport Psychology (PDF) (4th ed.). Wiley. pp. 121–157. doi:10.1002/9781119568124.ch7. ISBN   978-1-119-56807-0. S2CID   150348844.
9. Rabinowitz, L. (April 1936). "Does Midrash Tillim Reflect the Triennial Cycle of Psalms?". The Jewish Quarterly Review. 26 (4): 349–368. doi:10.2307/1452095. JSTOR   1452095.
10. Yarchin, William (July 2015). "Is There an Authoritative Shape for the Hebrew Book Of Psalms? Profiling the Manuscripts of the Hebrew Psalter". Revue Biblique. 122 (3): 355–370. JSTOR   44092352.