A267693 - OEIS

A267693

Decimal expansion of 477/4237.

1, 1, 2, 5, 7, 9, 6, 5, 5, 4, 1, 6, 5, 6, 8, 3, 2, 6, 6, 4, 6, 2, 1, 1, 9, 4, 2, 4, 1, 2, 0, 8, 4, 0, 2, 1, 7, 1, 3, 4, 7, 6, 5, 1, 6, 4, 0, 3, 1, 1, 5, 4, 1, 1, 8, 4, 8, 0, 0, 5, 6, 6, 4, 3, 8, 5, 1, 7, 8, 1, 9, 2, 1, 1, 7, 0, 6, 3, 9, 6, 0, 3, 4, 9, 3, 0, 3, 7, 5, 2, 6, 5, 5, 1, 8, 0, 5, 5, 2, 2, 7, 7, 5, 5

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

In the Antikythera mechanism this constant represents the difference between the time it takes for the moon to return to perigee and the time it takes for the moon to come back to the same point in the zodiac, in a year's turn.

The discovery that the constant 0.112579655 is present in the Antikythera mechanism is due to Tony Freeth.

The prime numbers 19, 53, 127 and 223 are related to the number of teeth of some of the known 30 bronze gearwheels of the mechanism (see A240136).

The prime numbers 19, 53 and 223 appear in the formula of this constant. They are also the first three primes congruent to 19 mod 34 (see A142072), or in other words: the first three odd primes of the form 17*n+2 (see A140544).

The function of one or two gears with 63 teeth is unknown.

Note that in ancient astronomy a cycle of 126 days was known to be related to Mercury and also a cycle of 13*19 + 5 = 252 days related to Venus; both 126 and 252 are multiples of 63.

LINKS

Table of n, a(n) for n=0..103.

Tony Freeth, Decoding an ancient computer, Scientific American (dec 2009), p. 82.

Tony Freeth and Alexander Jones, The cosmos in the Antikythera mechanism, (2012).

Wikipedia, Antikythera mechanism

FORMULA

d = (18/223)*(53/38) = (9/223)*(53/19) = 477/4237.

EXAMPLE

0.11257965541656832664621194241208402171347651640311541...

MATHEMATICA

First@ RealDigits@ N[477/4237, 120] (* Michael De Vlieger, Jan 27 2016 *)

PROG