10.10.10 Binary Day and The Answer to Life Day

My wife's cousin, George Smith, put a number of interesting facts on his facebook page today  regarding 10.10.10   As George points out, when you look at 101010 as the binary representation of decimal 42, then it gets to be a really interesting day:

• The obvious one of month, day and year all being the same number.
• 101010 is 42
• Wikipedia states: The number 42 is in the novel The Hitchhiker's Guide to the Galaxy by Douglas Adams. The Answer to the Ultimate Question of Life, the Universe, and Everything is calculated by an enormous supercomputer over a period of 7.5 million years to be 42. According to the novel Mostly Harmless, 42 is the street address of Stavromula Beta. In 1994, Adams created the 42 Puzzle, a game based on the number 42.

As Wikipedia also points out about 42 decimal:

• Given 27 same-size cubes whose nominal values progress from 1 to 27, a 3×3×3 magic cube can be constructed such that every row, column, and corridor, and every diagonal passing through the center, comprises 3 cubes whose sum of values is 42.

• Forty-two is a pronic number and an abundant number; its prime factorization 2 · 3 · 7 makes it the second sphenic number and also the second of the form { 2 · 3 · r }. As with all sphenic numbers of this form, the aliquot sum is abundant by 12. 42 is also the second sphenic number to be bracketed by twin primes; 30 is also a pronic number and also rests between two primes. 42 has a 14 member aliquot sequence 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0 and is itself part of the aliquot sequence commencing with the first sphenic number 30. Further, 42 is the 10th member of the 3-aliquot tree.

• 42 is the product of the first three terms of Sylvester's sequence; like the first five such numbers it is also a primary pseudoperfect number.

• It is the sum of the totient function for the first eleven integers.

• It is a Catalan number. Consequently; 42 is the number of noncrossing partitions of a set of five elements, the number of triangulations of a heptagon, the number of rooted ordered binary trees with six leaves, the number of ways in which five pairs of nested parentheses can be arranged, etc.

• It is the reciprocal of a Bernoulli number.

• It is conjectured to be the scaling factor in the leading order term of the "sixth moment of the Riemann zeta function". In particular, Conrey & Ghosh have conjectured
  

  

  where the infinite product is over all prime numbers, p.^[1][2]

• It is the third pentadecagonal number. It is a meandric number and an open meandric number.

• Since the greatest prime factor of 42² + 1 = 1765 is 353 and thus more than 42 twice, 42 is a Størmer number.

• 42 is a perfect score on the USA Math Olympiad (USAMO)^[3] and International Mathematical Olympiad (IMO).^[4]

• In base 10, this number is a Harshad number and a self number, while it is a repdigit in base 4 (as 222).

• The eight digits of pi beginning from 242,422 places after the decimal point are 42424242.

• 42 is the expected number of throws of a (single) fair die until two sixes show up successively (for the first time).

In technology

• Magic numbers used by programmers:
  • The glyph, or character, corresponding to the number 42 in the ASCII character set, is *, the asterisk, commonly known as the wildcard character. For example, when used in a Unix command such as "rm -fr /*", * means "everything".
  • In the TIFF image file format, the second 16-bit word of every file is 42, which is used together with the first word to indicate byte order.
  • In the reiser4 file system, 42 is the inode number of the root directory.

• The GNU C Library, a set of standard routines available for use in computer programming, contains a function—memfrob()—which performs an XOR combination of a given variable and the binary pattern 00101010 (42) as an XOR cipher.

• 42 is the result given by the web search engines Wolfram Alpha, Google and Microsoft's Bing when the query "the answer to life the universe and everything" is entered as a search.