149 (number)

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← 148 149 150 →
Cardinal one hundred forty-nine
Ordinal 149th
(one hundred forty-ninth)
Factorization prime
Prime 35th
Divisors 1, 149
Greek numeral ΡΜΘ´
Roman numeral CXLIX
Binary 100101012
Ternary 121123
Senary 4056
Octal 2258
Duodecimal 10512
Hexadecimal 9516

149 (one hundred [and] forty-nine) is the natural number between 148 and 150.

Contents

In mathematics

149 is the 35th prime number, the first prime whose difference from the previous prime is exactly 10, [1] an emirp, and an irregular prime. [2] After 1 and 127, it is the third smallest de Polignac number, an odd number that cannot be represented as a prime plus a power of two. [3] More strongly, after 1, it is the second smallest number that is not a sum of two prime powers. [4]

It is a tribonacci number, being the sum of the three preceding terms, 24, 44, 81. [5]

There are exactly 149 integer points in a closed circular disk of radius 7, [6] and exactly 149 ways of placing six queens (the maximum possible) on a 5 × 5 chess board so that each queen attacks exactly one other. [7] The barycentric subdivision of a tetrahedron produces an abstract simplicial complex with exactly 149 simplices. [8]

The digits in 149 in decimal are the first 3 square numbers.

In sports

149 is the highest number of goals ever scored in one football match. For more information, see AS Adema 149–0 SO l'Emyrne.

See also

Related Research Articles

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It is:

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References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA001632(Smallest prime p such that there is a gap of 2n between p and previous prime)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Metsänkylä, Tauno (1976). "Distribution of irregular prime numbers". Journal für die Reine und Angewandte Mathematik . 1976 (282): 126–130. doi:10.1515/crll.1976.282.126. MR   0399014. S2CID   201061944.
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA006285(Odd numbers not of form p + 2^k (de Polignac numbers))". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA071331(Numbers having no decomposition into a sum of two prime powers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. ↑ Schoen, Robert (1984). "Harmonic, geometric, and arithmetic means in generalized Fibonacci sequences" (PDF). The Fibonacci Quarterly . 22 (4): 354–357. MR   0766313.
  6. ↑ Sloane, N. J. A. (ed.). "SequenceA000328(Number of points of norm ≤ n^2 in square lattice)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  7. ↑ Sloane, N. J. A. (ed.). "SequenceA051567". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  8. ↑ Sloane, N. J. A. (ed.). "SequenceA002050(Number of simplices in barycentric subdivision of n-simplex)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
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