by neufer » Mon Jun 26, 2017 10:59 am
RocketRon wrote:APOD Robot wrote:
is not only a candidate to have life, but intercommunicating life
-- although a preliminary search has found no obvious transmissions
What are the odds of any extra-terrestrial life actually having any "communication" capability. ??
https://oeis.org/A287148 wrote:
Sequence A287148: Number of compositions (ordered partitions) of 2n-1 into
primes of form x2 + y2 (A002313). In other words: a(n) is the number of compositions of the n-th odd number into
primes of form x2 + y2.
0, 0, 1,
2, 3, 4, 6, 9, 15, 24, 37, 58, 92, 149, 243, 393, 629, 1004, 1603, 2564, 4106, 6571, 10508, 16807, 26895, 43060, 68952, 110392, 176696, 282798
Note that by definition a(4)..a(10) =
[2, 3, 4, 6, 9, 15, 24] is the number of compositions (ordered partitions) of
[7, 9, 11, 13, 15, 17, 19] respectively, into
primes of form x2 + y2. On the other hand a(4)..a(10) =
[2, 3, 4, 6, 9, 15, 24] is also the number of laps related to the orbital resonances of the seven Earth-sized planets
[h, g, f, e, d, c, b] in the planetary system of the TRAPPIST-1 star.>>
https://en.wikipedia.org/wiki/TRAPPIST-1 wrote:
<<The orbital motions of the TRAPPIST-1 planets form a complex chain with three-body Laplace-type resonances linking every member. The relative orbital periods (proceeding outward) approximate whole integer ratios of
24/24, 24/15, 24/9, 24/6, 24/4, 24/3, and 24/2, respectively, or nearest-neighbor period ratios of about 8/5, 5/3, 3/2, 3/2, 4/3, and 3/2 (1.603, 1.672, 1.506, 1.509, 1.342, and 1.519). This represents the longest known chain of near-resonant exoplanets, and is thought to have resulted from interactions between the planets as they migrated inward within the residual protoplanetary disk after forming at greater initial distances. The resonant chain has been shown to be necessary to keep the tightly packed system stable for long timescales, and the tight correspondence between whole number ratios in orbital resonances and in music theory has made it possible to convert the system's motion into music.>>
[quote="RocketRon"][quote="APOD Robot"]
is not only a candidate to have life, but intercommunicating life
-- although a preliminary search has found no obvious transmissions[/quote]
What are the odds of any extra-terrestrial life actually having any "communication" capability. ??[/quote][quote=" https://en.wikipedia.org/wiki/Contact_(novel)"]
[size=135]<<[i]"Project Argus" discovers a repeating series of [b][u][color=#FF00FF][the first] 26 prime numbers[/color][/u][/b] coming from the Vega system 25 light years away.[/i]>>[/size][/quote][quote=" https://oeis.org/A287148"]
[b][u][color=#FF0000]Sequence A287148[/color][/u][/b]: Number of compositions (ordered partitions) of 2n-1 into [b][u][color=#FF00FF]primes of form x[sup]2[/sup] + y[sup]2[/sup][/color][/u][/b] (A002313). In other words: a(n) is the number of compositions of the n-th odd number into [b][u][color=#FF00FF]primes of form x[sup]2[/sup] + y[sup]2[/sup][/color][/u][/b].
0, 0, 1, [b][u][color=#FF0000]2, 3, 4, 6, 9, 15, 24[/color][/u][/b], 37, 58, 92, 149, 243, 393, 629, 1004, 1603, 2564, 4106, 6571, 10508, 16807, 26895, 43060, 68952, 110392, 176696, 282798
Note that by definition a(4)..a(10) = [b][u][color=#FF0000][2, 3, 4, 6, 9, 15, 24][/color][/u][/b] is the number of compositions (ordered partitions) of [b][u][color=#0000FF][7, 9, 11, 13, 15, 17, 19][/color][/u][/b] respectively, into [b][u][color=#FF00FF]primes of form x[sup]2[/sup] + y[sup]2[/sup][/color][/u][/b]. On the other hand a(4)..a(10) = [b][u][color=#FF0000][2, 3, 4, 6, 9, 15, 24][/color][/u][/b] is also the number of laps related to the orbital resonances of the seven Earth-sized planets [b][u][color=#FF0000][h, g, f, e, d, c, b][/color][/u][/b] in the planetary system of the TRAPPIST-1 star.>>[/quote][quote=" https://en.wikipedia.org/wiki/TRAPPIST-1"]
<<The orbital motions of the TRAPPIST-1 planets form a complex chain with three-body Laplace-type resonances linking every member. The relative orbital periods (proceeding outward) approximate whole integer ratios of [b][u][color=#FF0000]24/24, 24/15, 24/9, 24/6, 24/4, 24/3, and 24/2[/color][/u][/b], respectively, or nearest-neighbor period ratios of about 8/5, 5/3, 3/2, 3/2, 4/3, and 3/2 (1.603, 1.672, 1.506, 1.509, 1.342, and 1.519). This represents the longest known chain of near-resonant exoplanets, and is thought to have resulted from interactions between the planets as they migrated inward within the residual protoplanetary disk after forming at greater initial distances. The resonant chain has been shown to be necessary to keep the tightly packed system stable for long timescales, and the tight correspondence between whole number ratios in orbital resonances and in music theory has made it possible to convert the system's motion into music.>>[/quote]