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## Main Question or Discussion Point

Are irrationals effective (seeded) random number input streams? E.g., here's 17

4.123105625617660549821409855974077025147199225373620434398633573094954346337621593587863650810684296684544040939214141615301420840415868363079548145746906977677023266436240863087790567572385708225521380732563083860309142749804671913529322147978718167815796475906080565496973900766721383689212106708921029005520264976997227788461399259924591373145657819254743622377232515783073400662476891460894993314102436279443386280552637475060905080869257482675403757576927464631666351033096817122919874195864431971054705958485725931943603620656058152613585046428067872150064104914222367522243486737258047037771274998566571218570432100303602606506487154690698281546846459564503441849930597639509078619959043334207783036732466105002383305603648597891517738125149725101393295630516977396156134483704021469549517283774775128332086775432479301964503858945967736521957022356481292823232373091650044755709460165721749143175547451122718361635317492475624065195560022755934398822460451518623945769412122844523427764255912670433259808358492948699826803953313743117174259527446589487487995234588945341405362382216244897199383951723677736924815737740851390093874931215463256061131831025557439033296612065618997712372326637094637265748287231103821317707944772530780064797150678855818398908582322952162045692531561131920561778167348673892987498555458433124657440601285674187836856748287375368481499912380912509688262497561558561564648512481411215339812008301990104085930861062338067167258928822842126024770742381463219000159897259624750259093195821477134731917698441102319595010755969064406071469393642506505486427451376148387657994040157094448093988829687785599616740434885132269481081155527404578852192449351277914392107618272900599754897954312002170599256849466159387615532763790999551021418146407027743000792920490048243451252056874608711185472125959950450945481146458616792396812655520824304951486086333901135640630166910365347510269977305391756449457931367201466774922328035237350342552906155151563822733055685642499595284430373695550870606523686673143876906178092044034814292694187010803880108829021799880687696158697329126877696593420355145932219374892438065025680057784508087680163993195284779117186081306592021305623343958242917631701153763240709357137139143819622153188015764287100179012418273573753050688530502962200477947919154553842693338844717836001761469185048394692345476131766736808878375874811980697221956669693993181703367244994221297365315344095040553005626348185982780376611654361701359383702910820779

It seems to satisfy randomness: e.g., .5 bit on/off probability, (provably) non-repeating, values evenly distributed; but will this continue to be the case as it's taken to infinite decimal places?

^{1/2}to 2496 (8K bits) decimal places:4.123105625617660549821409855974077025147199225373620434398633573094954346337621593587863650810684296684544040939214141615301420840415868363079548145746906977677023266436240863087790567572385708225521380732563083860309142749804671913529322147978718167815796475906080565496973900766721383689212106708921029005520264976997227788461399259924591373145657819254743622377232515783073400662476891460894993314102436279443386280552637475060905080869257482675403757576927464631666351033096817122919874195864431971054705958485725931943603620656058152613585046428067872150064104914222367522243486737258047037771274998566571218570432100303602606506487154690698281546846459564503441849930597639509078619959043334207783036732466105002383305603648597891517738125149725101393295630516977396156134483704021469549517283774775128332086775432479301964503858945967736521957022356481292823232373091650044755709460165721749143175547451122718361635317492475624065195560022755934398822460451518623945769412122844523427764255912670433259808358492948699826803953313743117174259527446589487487995234588945341405362382216244897199383951723677736924815737740851390093874931215463256061131831025557439033296612065618997712372326637094637265748287231103821317707944772530780064797150678855818398908582322952162045692531561131920561778167348673892987498555458433124657440601285674187836856748287375368481499912380912509688262497561558561564648512481411215339812008301990104085930861062338067167258928822842126024770742381463219000159897259624750259093195821477134731917698441102319595010755969064406071469393642506505486427451376148387657994040157094448093988829687785599616740434885132269481081155527404578852192449351277914392107618272900599754897954312002170599256849466159387615532763790999551021418146407027743000792920490048243451252056874608711185472125959950450945481146458616792396812655520824304951486086333901135640630166910365347510269977305391756449457931367201466774922328035237350342552906155151563822733055685642499595284430373695550870606523686673143876906178092044034814292694187010803880108829021799880687696158697329126877696593420355145932219374892438065025680057784508087680163993195284779117186081306592021305623343958242917631701153763240709357137139143819622153188015764287100179012418273573753050688530502962200477947919154553842693338844717836001761469185048394692345476131766736808878375874811980697221956669693993181703367244994221297365315344095040553005626348185982780376611654361701359383702910820779

It seems to satisfy randomness: e.g., .5 bit on/off probability, (provably) non-repeating, values evenly distributed; but will this continue to be the case as it's taken to infinite decimal places?