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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, 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 7 × 7 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]

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. doi:10.1080/00150517.1984.12429874. 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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