111 (number)

Number 111 the 1919 film Number 111 (1919 film) the 1938 film Number 111 (1938 film) the emergency telephone number in New Zealand 111 (New Zealand telephone number) 111 (disambiguation) April 2022 111 1, 3, 37, 111 111 (one hundred [and] eleven) is the natural number following 110 and preceding 112. In mathematics 111 is the fourth non-trivial nonagonal number,A001106 9-gonal (or enneagonal or nonagonal) numbers 2016-05-26 and the seventh perfect totient number.A082897 Perfect totient numbers 2016-05-26 111 is furthermore the ninth number such that its Euler totient of 72 is equal to the totient value of its sum-of-divisors: A006872 Numbers k such that phi(k) is phi(sigma(k)). 2024-02-03 Two other of its multiples (333 and 555) also have the same property (with totients of 216 and 288, respectively).Also,The 111th composite number 146A002808 The composite numbers: numbers n of the form x*y for x > 1 and y > 1. 2024-02-03 is the twelfth number whose totient value is the same value held by its sum-of-divisors. The sequence of nonagonal numbers that precede 111 is {0, 1, 9, 24, 46, 75}, members which add to 146 (without including 9). 357, in turn the index of 444 as a composite, is the twentieth such number, following 333. The composite index of 1000 is 831, the thirty-fifth member in this sequence of numbers to have a totient also shared by its sum-of-divisors, where 1000 is 1 + 999. The only two numbers in decimal less than 1000 whose prime factorisations feature primes concatenated into a new prime are 138 and 777 (as 2 × 3 × 23 and 3 × 7 × 37, respectively), which add to 915. This sum represents the 38th member in the aforementioned sequence. Magic squares 261px|thumb|111 is adjacent to 110 and 112, the minimal side lengths of perfect squared squares that are tiled by smaller squares of distinct side lengths. The smallest magic square using only 1 and prime numbers has a magic constant of 111:Dudeney Henry E. Henry Dudeney Amusements in Mathematics Thomas Nelson & Sons, Ltd. London 1917 125 https://djm.cc/library/Amusements_in_Mathematics_Dudeney_edited02.pdf 1667871 3173713376167143 Also, a six-by-six magic square using the numbers 1 to 36 also has a magic constant of 111: 111312919202222425830333262317934271012217351415161813364562832 (The square has this magic constant because 1 + 2 + 3 + ... + 34 + 35 + 36 = 666, and 666 / 6 = 111).Relatedly, 111 is also the magic constant of the n-Queens Problem for n = 6.A006003 a(n) = n*(n^2 + 1)/2 On the other hand, 111 lies between 110 and 112, which are the two smallest edge-lengths of squares that are tiled in the interior by smaller squares of distinct edge-lengths (see, squaring the square).Gambini Ian A method for cutting squares into distinct squares Discrete Applied Mathematics 98 1–2 Elsevier Amsterdam 65–80 1999 10.1016/S0166-218X(99)00158-4 free 1723687 0935.05024 Properties in certain radices 111 is or the second repunit in decimal,A002275 Repunits: (10^n - 1)/9. Often denoted by R_n. a number like 11, 111, or 1111 that consists of repeated units, or ones. 111 equals 3 × 37, therefore all triplets (numbers like 222 or 777) in base ten are repdigits of the form . As a repunit, it also follows that 111 is a palindromic number. All triplets in all bases are multiples of 111 in that base, therefore the number represented by 111 in a particular base is the only triplet that can ever be prime. 111 is not prime in decimal, but is prime in base two, where 1112 = 710. It is also prime in many other bases up to 128 (3, 5, 6, ..., 119) A002384. In base 10, it is furthermore a strobogrammatic number,A000787 Strobogrammatic numbers 2022-05-07 as well as a Harshad number.A005349 Niven (or Harshad) numbers 2016-05-26 In base 18, the number 111 is 73 (= 34310) which is the only base where 111 is a perfect power. See also 111 is the atomic number of roentgenium. The number 111 is called a Nelson in cricket, famously considered unlucky by umpire David Shepherd.2003-04-12 David Shepherd's Umpire Guide http://news.bbc.co.uk/sport2/hi/cricket/2929691.stm 2026-09-30 en-GB Notes References Further reading Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134 External links 1 Category:Integers