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What is the longest known sequence that repeats in Pi? (homelab)
Math: Interesting problems in computational number theory for the Homelab. What is the longest known sequence of numbers that repeats in Pi? Have you ever wondered what numbers repeat in the known decimal representation of Pi? A quick look at Pi reveals a few obvious answers: 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315 The first and most obvious repeat is a single digit, 1, which repeats in the first 3 digits of Pi.
We could subtract ‘0’ from these so they are simple byte values, but it doesn’t make large difference in execution time. This entire process could be optimized significantly with some better inline code, a reduction in math operations, and some memory footprint tweaking. They often cover these kinds of computational number theory topics as well as a host of other really interesting mathematical tangents!
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