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.[27][28]
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.[31] 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.[32] 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[7] (the
cousin prime to 13),[8]7 is the
prime index of 17.[6] 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.[9]
The reduced Collatz sequence of 27, that counts the number of prime numbers in its trajectory, is
41.[11] 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).[3][2]
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),[12] 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.
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.[27][28]
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.[31] 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.[32] 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[7] (the
cousin prime to 13),[8]7 is the
prime index of 17.[6] 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.[9]
The reduced Collatz sequence of 27, that counts the number of prime numbers in its trajectory, is
41.[11] 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).[3][2]
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),[12] 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.