Math curiosity: expansion of 1/998001

1/998001 = 0.0000010020030040050060070080090100110120130140150160170180190200210
22023024025026027028029030031032033034035036037038039040041042043044045046047048
04905005105205305405505605705805906006106206306406506606706806907007107207307407
50760770780790800810820830840850860870880890900910920930940950960970980991001011
02103104105106107108109110111112113114115116117118119120121122123124125126127128
12913013113213313413513613713813914014114214314414514614714814915015115215315415
51561571581591601611621631641651661671681691701711721731741751761771781791801811
82183184185186187188189190191192193194195196197198199200201202203204205206207208
20921021121221321421521621721821922022122222322422522622722822923023123223323423
52362372382392402412422432442452462472482492502512522532542552562572582592602612
62263264265266267268269270271272273274275276277278279280281282283284285286287288
28929029129229329429529629729829930030130230330430530630730830931031131231331431
53163173183193203213223233243253263273283293303313323333343353363373383393403413
42343344345346347348349350351352353354355356357358359360361362363364365366367368
36937037137237337437537637737837938038138238338438538638738838939039139239339439
53963973983994004014024034044054064074084094104114124134144154164174184194204214
22423424425426427428429430431432433434435436437438439440441442443444445446447448
44945045145245345445545645745845946046146246346446546646746846947047147247347447
54764774784794804814824834844854864874884894904914924934944954964974984995005015
02503504505506507508509510511512513514515516517518519520521522523524525526527528
52953053153253353453553653753853954054154254354454554654754854955055155255355455
55565575585595605615625635645655665675685695705715725735745755765775785795805815
82583584585586587588589590591592593594595596597598599600601602603604605606607608
60961061161261361461561661761861962062162262362462562662762862963063163263363463
56366376386396406416426436446456466476486496506516526536546556566576586596606616
62663664665666667668669670671672673674675676677678679680681682683684685686687688
68969069169269369469569669769869970070170270370470570670770870971071171271371471
57167177187197207217227237247257267277287297307317327337347357367377387397407417
42743744745746747748749750751752753754755756757758759760761762763764765766767768
76977077177277377477577677777877978078178278378478578678778878979079179279379479
57967977987998008018028038048058068078088098108118128138148158168178188198208218
22823824825826827828829830831832833834835836837838839840841842843844845846847848
84985085185285385485585685785885986086186286386486586686786886987087187287387487
58768778788798808818828838848858868878888898908918928938948958968978988999009019
02903904905906907908909910911912913914915916917918919920921922923924925926927928
92993093193293393493593693793893994094194294394494594694794894995095195295395495
595695795895996096196296396496596696796896997097197297397497

Note that the result contains the sequence “000”, “111”, “222” up to “999” (with exception of “998”), after which it starts again. This expansion was obtained evaluating the expression 1 + (1/999^2).n(digits = 3007) with the help of Sage Online (sagenb.org). A “1” was added to the expression to show the first zeroes, otherwise Sage uses exponential notation and omits them.

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