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147 (number)

From Wikipedia, the free encyclopedia
Natural number
← 146147 148 →
Cardinalone hundred forty-seven
Ordinal147th
(one hundred forty-seventh)
Factorization3 × 72
Divisors1, 3, 7, 21, 49, 147
Greek numeralΡΜΖ´
Roman numeralCXLVII,cxlvii
Binary100100112
Ternary121103
Senary4036
Octal2238
Duodecimal10312
Hexadecimal9316

147 (one hundred [and] forty-seven) is thenatural number following146 and preceding148.

In mathematics

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147 is the fourthcentered icosahedral number. These are a class offigurate numbers that represent points in the shape of aregular icosahedron or alternatively points in the shape of acuboctahedron, and aremagic numbers for theface-centered cubic lattice.[1] Separately, it is also a magic number for thediamond cubic.[2]

It is also the fourth Apéry numbera3{\displaystyle a_{3}} following19, where[3]an=k=0n(nk)2(n+kk),{\displaystyle a_{n}=\sum _{k=0}^{n}{\binom {n}{k}}^{2}{\binom {n+k}{k}},}

with 147 thecomposite index of the nineteenthtriangle number,190.[4][5]

There are 147 different ways of representing one as asum of unit fractions with five terms, allowing repeated fractions,[6] and 147 different self-avoidingpolygonal chains of length six using horizontal and vertical segments of theinteger lattice.[7]

See also

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References

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  1. ^Sloane, N. J. A. (ed.)."Sequence A005902 (Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^Sloane, N. J. A. (ed.)."Sequence A007904 (Crystal ball sequence for diamond)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^Sloane, N. J. A. (ed.)."Sequence A005258 (Apéry numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^Sloane, N. J. A. (ed.)."Sequence A002808 (The composite numbers: numbers n of the form x*y for x > 1 and y > 1.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2023-12-29.
  5. ^Sloane, N. J. A. (ed.)."Sequence A000217 (Triangular number: a(n) is the binomial(n+1,2) equivalent to n*(n+1)/2 that is 0 + 1 + 2 + ... + n.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2023-12-29.
  6. ^Sloane, N. J. A. (ed.)."Sequence A002966 (Egyptian fractions: number of solutions of 1 = 1/x_1 + ... + 1/x_n where 0 < x_1 ≤ ... ≤ x_n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^Sloane, N. J. A. (ed.)."Sequence A037245 (Number of unrooted self-avoiding walks of n steps on square lattice)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
0 to 199
200 to 399
400 to 999
1000s and 10,000s
1000s
10,000s
100,000s to 10,000,000,000,000s
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