227 (number)
| ||||
|---|---|---|---|---|
| Cardinal | two hundred twenty-seven | |||
| Ordinal | 227th (two hundred twenty-seventh) | |||
| Factorization | prime | |||
| Prime | yes | |||
| Greek numeral | ΣΚΖ´ | |||
| Roman numeral | CCXXVII | |||
| Binary | 111000112 | |||
| Ternary | 221023 | |||
| Senary | 10156 | |||
| Octal | 3438 | |||
| Duodecimal | 16B12 | |||
| Hexadecimal | E316 | |||
227 (two hundred [and] twenty-seven) is the natural number between 226 and 228. It is also a prime number.
In mathematics[edit]
227 is the 49th prime number, an index whose value is a square number (72). It is a twin prime, and the start of a prime triplet (with 229 and 233).[1]
It is a safe prime, as dividing it by two and rounding down produces the Sophie Germain prime, 113.[2] It is also:
- a regular prime,[3]
- a Pillai prime,[4]
- a Stern prime,[5] and
- a Ramanujan prime.[6]
227 and 229 form the first twin prime pair for which neither is a cluster prime.
The 227th harmonic number is the first to exceed 6.[7]
There are 227 different connected graphs with eight edges,[8] and 227 independent sets in a 3 × 4 grid graph.[9]
Convergents to π[edit]
227 is the difference between 333 and 106, which are respectively the numerator and denominator in the fourth convergent to pi,[10][11] correct to four decimal places:
Meanwhile, the sum of the first few denominators in convergents to pi (1, 7, 106, 113)[11] yields 227.[a]
References[edit]
- ^ On the other hand, is the sum of the first forty-one distinct entries in the continued fraction for pi that precedes , the largest term up to that point (by two orders of magnitude).[12]
- ^ Sloane, N. J. A. (ed.). "Sequence A022004 (Initial members of prime triples (p, p+2, p+6))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007703 (Regular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A063980 (Pillai primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A042978 (Stern primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A104272 (Ramanujan primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002387 (Least k such that H(k) > n, where H(k) is the harmonic number sum_{i=1..k} 1/i)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002905 (Number of connected graphs with n edges)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A051736 (Number of 3 x n (0,1)-matrices with no consecutive 1's in any row or column)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002485 (Numerators of convergents to Pi.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-06-14.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A002486 (Apart from two leading terms (which are present by convention), denominators of convergents to Pi (A002485 and A046947 give numerators).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-06-14.
- ^ Sloane, N. J. A. (ed.). "Sequence A154883 (Distinct entries in continued fraction for Pi in the order of their appearance.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-06-16.
 | This article about a number is a stub. You can help Wikipedia by expanding it. |