149 (number)

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

← 148 149 150 →
Cardinalone hundred forty-nine
Ordinal149th
(one hundred forty-ninth)
Factorizationprime
Prime35th
Divisors1, 149
Greek numeralΡΜΘ´
Roman numeralCXLIX
Binary100101012
Ternary121123
Senary4056
Octal2258
Duodecimal10512
Hexadecimal9516

In mathematics

149 is a 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]

See also

References
  1. Sloane, N. J. A. (ed.). "Sequence A001632 (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.). "Sequence A006285 (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.). "Sequence A071331 (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.). "Sequence A000328 (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.). "Sequence A051567". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. Sloane, N. J. A. (ed.). "Sequence A002050 (Number of simplices in barycentric subdivision of n-simplex)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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