Cannabaceae

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277 (two hundred [and] seventy-seven) is the natural number following 276 and preceding 278.

← 276 277 278 →
Cardinaltwo hundred seventy-seven
Ordinal277th
(two hundred seventy-seventh)
Factorizationprime
Primeyes
Greek numeralΣΟΖ´
Roman numeralCCLXXVII
Binary1000101012
Ternary1010213
Senary11416
Octal4258
Duodecimal1B112
Hexadecimal11516

Mathematical properties[edit]

277 is the 59th prime number, and is a regular prime.[1] It is the smallest prime p such that the sum of the inverses of the primes up to p is greater than two.[2] Since 59 is itself prime, 277 is a super-prime.[3] 59 is also a super-prime (it is the 17th prime), as is 17 (the 7th prime). However, 7 is the fourth prime number, and 4 is not prime. Thus, 277 is a super-super-super-prime but not a super-super-super-super-prime.[4] It is the largest prime factor of the Euclid number 510511 = 2 × 3 × 5 × 7 × 11 × 13 × 17 + 1.[5]

As a member of the lazy caterer's sequence, 277 counts the maximum number of pieces obtained by slicing a pancake with 23 straight cuts.[6] 277 is also a Perrin number, and as such counts the number of maximal independent sets in an icosagon.[7][8] There are 277 ways to tile a 3 × 8 rectangle with integer-sided squares,[9] and 277 degree-7 monic polynomials with integer coefficients and all roots in the unit disk.[10] On an infinite chessboard, there are 277 squares that a knight can reach from a given starting position in exactly six moves.[11]

277 appears as the numerator of the fifth term of the Taylor series for the secant function:[12]

Since no number added to the sum of its digits generates 277, it is a self number. The next prime self number is not reached until 367.[13]

References[edit]

  1. ^ Sloane, N. J. A. (ed.). "Sequence A007703 (Regular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A016088 (a(n) = smallest prime p such that Sum_{ primes q = 2, ..., p} 1/q exceeds n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A006450 (Primes with prime subscripts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Fernandez, Neil (1999), An order of primeness, F(p), archived from the original on 2012-07-10, retrieved 2013-09-11.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A002585 (Largest prime factor of 1 + (product of first n primes))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A000124 (Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence (or Ondrej Such sequence): a(n) = a(n-2) + a(n-3))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^ Füredi, Z. (1987), "The number of maximal independent sets in connected graphs", Journal of Graph Theory, 11 (4): 463–470, doi:10.1002/jgt.3190110403.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A002478 (Bisection of A000930)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A051894 (Number of monic polynomials with integer coefficients of degree n with all roots in unit disc)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. ^ Sloane, N. J. A. (ed.). "Sequence A118312 (Number of squares on infinite chessboard that a knight can reach in n moves from a fixed square)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  12. ^ Sloane, N. J. A. (ed.). "Sequence A046976 (Numerators of Taylor series for sec(x) = 1/cos(x))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  13. ^ Sloane, N. J. A. (ed.). "Sequence A006378 (Prime self (or Colombian) numbers: primes not expressible as the sum of an integer and its digit sum)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
source: https://en.wikipedia.org/wiki/277_(number)

One thought on “Cannabaceae”

  1. Well, that’s interesting to know that Psilotum nudum are known as whisk ferns. Psilotum nudum is the commoner species of the two. While the P. flaccidum is a rare species and is found in the tropical islands. Both the species are usually epiphytic in habit and grow upon tree ferns. These species may also be terrestrial and grow in humus or in the crevices of the rocks.
    View the detailed Guide of Psilotum nudum: Detailed Study Of Psilotum Nudum (Whisk Fern), Classification, Anatomy, Reproduction

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