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Audioactive Sequences

LALataliat•Created September 6, 2015
Audioactive Sequences
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Instructions

A puzzle! Can YOU figure out the trick? Use turbo mode please. (not necessary though) Press the arrow keys on screen, or arrow keys on keyboard, to change what spot of the sequence is being displayed.

Description

John Conway was the one who studied this extensively. I read something about it and thought I'd share it because it's really cool! I reccomend you read more on these (also known as "look and say sequences") because they have tight connections to science and algebra. It made me laugh for some reason when I found out that Conway's Constant (approximately 1.30357...; when raised to the power of N, answer will equal approximately the number of digits in the Nth spot of the "Look and see" sequence) is the only positive real root of the polynomial function: x^71 - x^69 - 2x^68 - x^67 + 2x^66 + 2x^65 + x^64 - x^63 - x^62 - x^61 - x^60 - x^59 + 2x^58 + 5x^57 + 3x^56 - 2x^55 - 10x^54 - 3x^53 - 2x^52 + 6x^51 + 6x^50 + x^49 + 9x^48 - 3x^47 - 7x^46 - 8x^45 - 8x^44 + 10x^43 + 6x^42 + 8x^41 - 5x^40 - 12x^39 + 7x^38 - 7x^37 + 7x^36 + x^35 - 3x^34 + 10x^33 + x^32 - 6x^31 - 2x^30 -10x^29 - 3x^28 + 2x^27 + 9x^26 - 3x^25 + 14x^24 - 8x^23 - 7x^21 + 9x^20 + 3x^19 - 4x^18 - 10x^17 - 7x^16 + 12x^15 + 7x^14 + 2x^13 - 12x^12 - 4x^11 - 2x^10 + 5x^9 + x^7 - 7x^6 + 7x^5 - 4x^4 + 12x^3 - 6x^2 + 3x - 6 = 0 ...!! If I didn't value my graphing calculator, I think I might attempt to graph it -- but for now I think I'll hold off! And yes I noticed I spelled "audioactive" as "adioactive." Japanese spelling is really getting to me... I did think something looked wrong though, just couldn't pinpoint. Oh and there's no 'i'

Project Details

Project ID75557196
CreatedSeptember 6, 2015
Last ModifiedJune 6, 2016
SharedSeptember 7, 2015
Visibilityvisible
CommentsAllowed