149 (number)
| ||||
|---|---|---|---|---|
| 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 forty-nine) is the natural number between 148 and 150.
In mathematics
149 is the 35th prime number, the first prime whose difference from the previous prime is exactly 10, an emirp, and an irregular prime. 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. More strongly, after 1, it is the second smallest number that is not a sum of two prime powers.
It is a tribonacci number, being the sum of the three preceding terms, 24, 44, 81.
There are exactly 149 integer points in a closed circular disk of radius 7, 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. The barycentric subdivision of a tetrahedron produces an abstract simplicial complex with exactly 149 simplices.
See also
- The year AD 149 or 149 BC
- List of highways numbered 149
- All pages with titles containing 149
References
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ Schoen, Robert (1984). "Harmonic, geometric, and arithmetic means in generalized Fibonacci sequences" (PDF). The Fibonacci Quarterly. 22 (4): 354–357. MR 0766313.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A051567". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
External links
