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Prévost Constant

2560 Decimals of the Sum of the
Reciprocals of Fibonacci Numbers
(a number shown to be irrational by Marc Prévost c. 1977)

1/1 + 1/1 + 1/2 + 1/3 + 1/5 + 1/8 + 1/13 + 1/21 + 1/34 + 1/55 + 1/89 + ...   =

  3. 3598856662 4317755317 2011302918 9271796889 0513373196 8486495553 8153251303 1899668338 3615416216 4567900872 9704534292 8853913304 1367890171 0088367959 1351733077 1190785803 3355033250 7753187599 8504871797 7789700603 9564509215 3758927752 6567335402 4033169441 7992939346 1099262625 7964647651 8686594497 1021655898 4360881472 6932495910 7947387367 3378523326 8774997627 2775794685 3676918541 9814676687 4299876738 2096913901 2177220244 0520815109 4264934951 3745416672 7895534447 0777775847 8025963407 6907484741 5557910420 0675015203 4107053352 8512979263 5242062267 5375680557 6195566972 0848843854 4079833242 9285136807 0827522662 5797511886 4646409673 7461572387 2362955620 5361220302 4635409252 6784242243 4703631036 3201466298 0402490155 7872445617 6000319551 9879059699 4202917886 6949174808 0967465236 8265408693 8399069873 2117521669 5706385941 1814553647 3642687824 6292616665 0100098903 8048233595 1989314615 0108288726 3928876699 1714930405 3057745574 3215611672 9898561772 9731395370 7352919668 8432789802 2165047585 0280918062 9100244427 7017460241 0404177860 6919006503 7142835294 2454906015 9304435523 6839237185 0498719863 0763391594 9365961429 8835472459 0992947082 6722312017 2721663872 1241823194 2461961057 7520161527 4957788183 2442620171 3211933554 2401421132 2226700585 0779033680 5573465162 5058402299 0863875041 5257469368 2112471825 6844645556 0163162771 3455714375 1455007624 8709915618 2826892640 7729981514 7332688964 9615571449 2245865861 3241975424 9306781786 2593585541 9053397178 9150545558 6364455620 7938031405 8450581455 4507217415 5386643901 3072379329 3693324593 4080446768 6577840688 8082567405 1153703481 6565354065 6305697845 3326208049 9053683459 7514423561 1198399264 7704742776 9803101105 8815581718 4923932868 9438984433 2490569195 4917268760 9559508041 2484819283 2597163873 0802925381 9599769804 1544855121 7281602262 0331943066 6297327595 3192227665 9735532353 6048195252 1028670014 2139979788 4243553601 6795991220 4261837046 1574804015 1050250099 9175943684 6692219596 0627316577 6487679414 8052152436 3689518527 4413814062 6600534344 1160130978 5072730856 4103745364 9905644909 2564022479 2358931548 7176694924 3670359504 3022373000 3069311959 1523084241 2942958779 7826500093 7094948239 5881794956 5175795285 9542579393 8129592869 0136021009 4380436689 5230969934 1361290441 7034628264 1703783983 5745622337 0388719700 9716007655 7065423903 8874719113 5079115407 6113460540 5981579190 2305756264 6715753591 6491877701 4875545821 8502626932 4924055408 5215622504 4719698236 6623355498 6281689696 6683627789 0783224455 2306778661 1861907014 6699590190 4809618163 9899148842 7181733025 7799164004 7704791863 4507268563 9394496425 9507568329 2036957858 7382609087 7061694844 3545099148 6528604325 6563839001 6063340306 1156303539 6354098363 2188358344 7308088390+

Continued Fraction Expansion:

[ 3 ; 3, 2, 1, 3, 1, 1, 13, 2, 3, 3, 2, 1, 1, 6, 3, 2, 4, 362, 2, 4, 8, 6, 30, 50, 1, 6, 3, 3, 2, 7, 2, 3, 1, 3, 2, 1, 1, 1, 1, 3, 4, 1, 1, 1, 172, 3, 26, 1, 18, 8, 2, 1, 1, 2, 8, 2, 72, 2, 3, 1, 1, 1, 1, 5, 2, 33, 1, 2, 52, 1, 3, 5, 1, 11, 1, 1, 3, 13, 2, 2, 4, 2, 14, 4, 1, 1, 10, 4, 4, 3, 5, 17, 3, 4, 2, 4, 1, 312, 2, 5, 1, 1, 3, 6, 8, 2, 31, 8, 9, 1, 3, 1, 1, 1, 6, 1, 1, 4, 1, 2, 1, 1, 5, 2, 1, 1, 2, 1, 1, 1, 15, 2, 1, 5, 2, 4, 6, 15, 2, 1, 1, 1, 1, 5, 2, 2, 1, 38, 1, 1, 1, 2, 3, 3, 1, 9, 6, 1, 1, 6, 1, 68, 1, 2, 1, 1, 20, 5, 2, 1, 2, 2, 5, 1, 2, 2, 1, 2, 3, 2, 1, 16, 1, 1, 1, 13, 1, 1, 1, 1, 2, 1, 1, 1, 13, 2, 59, 12, 19, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 5, 11, 1, 1, 1, 18, 7, 1, 5, 4, 165, 7, 1, 4, 1, 1, 3, 1, 1, 2, 2, 4, 2, 1, 3, 6, 2, 3, 4, 1, 2, 3, 1, 1, 1, 187, 1, 8, 3, 18, 1, 7, 3, 4, 2, 7, 2, 5, 1, 4, 2, 12, 2, 35, 1, 1, 1, 4, 7, 1, 3, 265, 3, 1, 1, 1, 1, 1, 2, 2, 2, 1, 11, 1, 1, 3, 1, 4, 1, 1, 4, 1, 3, 3, 10, 1, 2, 9, 1, 4, 15, 4, 1, 27, 1, 1, 48, 2, 3, 1, 1, 1, 1, 1, 370, 1, 8, 1, 2, 3, 6, 1, 1, 3, 12, 1, 14, 2, 1, 4, 4, 2, 1, 6, 2, 8, 6, 1, 2, 1, 11, 2, 2, 2, 1, 1, 21, 1, 3, 5, 2, 1, 4, 3, 5, 3, 1, 29, 1, 1, 205, 1, 2, 1, 8, 1, 5, 4, 3, 1, 3, 1, 2, 12, 14, 7, 7, 1, 8, 3, 1, 1, 6, 21, 5, 1, 51, 7, 2, 1, 1, 12, 1, 9, 3, 1, 1, 8, 1, 1, 2, 1, 2, 1, 1, 2, 2, 18, 1, 13, 6, 24, 24, 2, 1, 1, 4, 2, 4, 3, 8, 10, 1, 4, 2, 1, 12, 1, 5, 1, 1, 1, 1, 4, 2, 2, 1, 7, 2, 1, 1, 68, 1, 1, 2, 1, 13, 7, 3, 1, 1, 18, 1, 4, 10, 2, 3, 1, 1, 1, 12, 1, 1, 1, 1, 28, 3, 2, 6, 1, 3, 2, 4, 4, 2, 1, 1, 3, 3, 2, 1, 1, 1, 5, 3, 1, 10, 3, 3, 1, 1, 2, 8, 1, 3, 7, 1, 6, 2, 2, 23, 2, 3, 17, 3, 3, 1, 3, 6, 6, 1, 45, 9, ...]
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