In this article, we will explore the fascinating world of 27 (number). From its origins to its impact on today's society, we will immerse ourselves in a detailed analysis that will allow us to understand its importance in different areas. 27 (number) has been the subject of interest and debate over time, its implications have transcended cultural and generational barriers. Through this journey, we will seek to unravel the mysteries and curiosities surrounding 27 (number), in an attempt to shed light on its relevance in the current context.
the only positive integer that is three times the sum of its digits,
equal to the sum of the numbers between and including its digits: .
Also in base ten, if one cyclically rotates the digits of a three-digit number that is a multiple of 27, the new number is also a multiple of 27. For example, 378, 783, and 837 are all divisible by 27.
In similar fashion, any multiple of 27 can be mirrored and spaced with a zero each for another multiple of 27 (i.e. 27 and 702, 54 and 405, and 378 and 80703 are all multiples of 27).
Any multiple of 27 with "000" or "999" inserted yields another multiple of 27 (20007, 29997, 50004, and 59994 are all multiples of 27).
In senary (base six), one can readily test for divisibility by 43 (decimal 27) by seeing if the last three digits of the number match 000, 043, 130, 213, 300, 343, 430, or 513.
In decimal representation, 27 is located at the twenty-eighth (and twenty-ninth) digit after the decimal point in π:
If one starts counting with zero, 27 is the second self-locating string after 6, of only a few known.
In science
The Moon revolves around the Earth the same direction as Earth spins but 27 (27.3) times slower.
The Saros number of the solar eclipse series, which began on March 9, 1993, BCE and ended on April 16, 713 BCE. The duration of Saros series 27 was 1,280.1 years, and it contained 72 solar eclipses. Further, the Saros number of the lunar eclipse series, which began on July 28, 1926, BCE and ended on January 23, 411 BCE. The duration of Saros series 27 was 1532.5 years, and it contained 86 lunar eclipses.
Electronics
The type 27 vacuum tube (valve), a triode introduced in 1927, was the first tube mass-produced for commercial use to incorporate an indirectly heated cathode. This made it the first vacuum tube that could function as a detector in AC-powered radios. Prior to the introduction of the 27, home radios were powered by a set of three or more storage batteries with voltages of 3 volts to 135 volts.
^Whereas the composite index of 27 is 17 (the cousin prime to 13),7 is the prime index of 17. The sum 27 + 17 + 7 = 53 represents the sixteenth indexed prime (where 42 = 16). While 7 is the fourth prime number, the fourth composite number is 9 = 32, that is also the composite index of 16.
The reduced Collatz sequence of 27, that counts the number of prime numbers in its trajectory, is 41. This count represents the thirteenth prime number, that is also in equivalence with the sum of members in the aliquot tree (27, 13, 1, 0).
The next two larger numbers in the Collatz conjecture to require more than 111 steps to return to 1 are 54 and 55
Specifically, the fourteenth prime number 43 requires twenty-seven steps to reach 1.
The sixth pair of twin primes is (41, 43), whose respective prime indices generate a sum of 27.
^Also, 36 = 62 is the sum between PTNs 39 – 15 = 24 and 3 + 9 = 12. In this sequence, 111 is the seventh PTN.
^ abSloane, N. J. A., ed. (January 11, 1975). "Aliquot sequences". Mathematics of Computation. 29 (129). OEIS Foundation: 101–107. Retrieved October 31, 2023.