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A267693 Decimal expansion of 477/4237. 0
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.

REFERENCES

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

LINKS

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

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

(PARI) 477/4237. \\ Charles R Greathouse IV, Apr 18 2016

CROSSREFS

Cf. A000040, A140544, A142072, A240136.

Sequence in context: A227445 A216968 A088757 * A070985 A246339 A104428

Adjacent sequences:  A267690 A267691 A267692 * A267694 A267695 A267696

KEYWORD

nonn,cons,easy

AUTHOR

Omar E. Pol, Jan 24 2016

STATUS

approved

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Last modified January 21 19:40 EST 2019. Contains 319350 sequences. (Running on oeis4.)