Fibonacci numbers
Recently there was a scripting challenge on the use-rev list to calculate the 211st number in the Fibonacci series.This uses Brian Yennie's script to get accurate results since basic addition overflows at a certain point.
Just for fun, I added a column to show how the ratio of adjacent numbers in this sequence approaches the Golden Ratio.
| # | Fibonacci | Ratio |
|---|---|---|
| 1 | 1 | |
| 2 | 1 | 1 |
| 3 | 2 | 2 |
| 4 | 3 | 1.5 |
| 5 | 5 | 1.666667 |
| 6 | 8 | 1.6 |
| 7 | 13 | 1.625 |
| 8 | 21 | 1.615385 |
| 9 | 34 | 1.619048 |
| 10 | 55 | 1.617647 |
| 11 | 89 | 1.618182 |
| 12 | 144 | 1.617978 |
| 13 | 233 | 1.618056 |
| 14 | 377 | 1.618026 |
| 15 | 610 | 1.618037 |
| 16 | 987 | 1.618033 |
| 17 | 1597 | 1.618034 |
| 18 | 2584 | 1.618034 |
| 19 | 4181 | 1.618034 |
| 20 | 6765 | 1.618034 |
| 21 | 10946 | 1.618034 |
| 22 | 17711 | 1.618034 |
| 23 | 28657 | 1.618034 |
| 24 | 46368 | 1.618034 |
| 25 | 75025 | 1.618034 |
| 26 | 121393 | 1.618034 |
| 27 | 196418 | 1.618034 |
| 28 | 317811 | 1.618034 |
| 29 | 514229 | 1.618034 |
| 30 | 832040 | 1.618034 |
| 31 | 1346269 | 1.618034 |
| 32 | 2178309 | 1.618034 |
| 33 | 3524578 | 1.618034 |
| 34 | 5702887 | 1.618034 |
| 35 | 9227465 | 1.618034 |
| 36 | 14930352 | 1.618034 |
| 37 | 24157817 | 1.618034 |
| 38 | 39088169 | 1.618034 |
| 39 | 63245986 | 1.618034 |
| 40 | 102334155 | 1.618034 |
| 41 | 165580141 | 1.618034 |
| 42 | 267914296 | 1.618034 |
| 43 | 433494437 | 1.618034 |
| 44 | 701408733 | 1.618034 |
| 45 | 1134903170 | 1.618034 |
| 46 | 1836311903 | 1.618034 |
| 47 | 2971215073 | 1.618034 |
| 48 | 4807526976 | 1.618034 |
| 49 | 7778742049 | 1.618034 |
| 50 | 12586269025 | 1.618034 |
| 51 | 20365011074 | 1.618034 |
| 52 | 32951280099 | 1.618034 |
| 53 | 53316291173 | 1.618034 |
| 54 | 86267571272 | 1.618034 |
| 55 | 139583862445 | 1.618034 |
| 56 | 225851433717 | 1.618034 |
| 57 | 365435296162 | 1.618034 |
| 58 | 591286729879 | 1.618034 |
| 59 | 956722026041 | 1.618034 |
| 60 | 1548008755920 | 1.618034 |
| 61 | 2504730781961 | 1.618034 |
| 62 | 4052739537881 | 1.618034 |
| 63 | 6557470319842 | 1.618034 |
| 64 | 10610209857723 | 1.618034 |
| 65 | 17167680177565 | 1.618034 |
| 66 | 27777890035288 | 1.618034 |
| 67 | 44945570212853 | 1.618034 |
| 68 | 72723460248141 | 1.618034 |
| 69 | 117669030460994 | 1.618034 |
| 70 | 190392490709135 | 1.618034 |
| 71 | 308061521170129 | 1.618034 |
| 72 | 498454011879264 | 1.618034 |
| 73 | 806515533049393 | 1.618034 |
| 74 | 1304969544928657 | 1.618034 |
| 75 | 2111485077978050 | 1.618034 |
| 76 | 3416454622906707 | 1.618034 |
| 77 | 5527939700884757 | 1.618034 |
| 78 | 8944394323791464 | 1.618034 |
| 79 | 14472334024676221 | 1.618034 |
| 80 | 23416728348467685 | 1.618034 |
| 81 | 37889062373143906 | 1.618034 |
| 82 | 61305790721611591 | 1.618034 |
| 83 | 99194853094755497 | 1.618034 |
| 84 | 160500643816367088 | 1.618034 |
| 85 | 259695496911122585 | 1.618034 |
| 86 | 420196140727489673 | 1.618034 |
| 87 | 679891637638612258 | 1.618034 |
| 88 | 1100087778366101931 | 1.618034 |
| 89 | 1779979416004714189 | 1.618034 |
| 90 | 2880067194370816120 | 1.618034 |
| 91 | 4660046610375530309 | 1.618034 |
| 92 | 7540113804746346429 | 1.618034 |
| 93 | 12200160415121876738 | 1.618034 |
| 94 | 19740274219868223167 | 1.618034 |
| 95 | 31940434634990099905 | 1.618034 |
| 96 | 51680708854858323072 | 1.618034 |
| 97 | 83621143489848422977 | 1.618034 |
| 98 | 135301852344706746049 | 1.618034 |
| 99 | 218922995834555169026 | 1.618034 |
| 100 | 354224848179261915075 | 1.618034 |
| 101 | 573147844013817084101 | 1.618034 |
| 102 | 927372692193078999176 | 1.618034 |
| 103 | 1500520536206896083277 | 1.618034 |
| 104 | 2427893228399975082453 | 1.618034 |
| 105 | 3928413764606871165730 | 1.618034 |
| 106 | 6356306993006846248183 | 1.618034 |
| 107 | 10284720757613717413913 | 1.618034 |
| 108 | 16641027750620563662096 | 1.618034 |
| 109 | 26925748508234281076009 | 1.618034 |
| 110 | 43566776258854844738105 | 1.618034 |
| 111 | 70492524767089125814114 | 1.618034 |
| 112 | 114059301025943970552219 | 1.618034 |
| 113 | 184551825793033096366333 | 1.618034 |
| 114 | 298611126818977066918552 | 1.618034 |
| 115 | 483162952612010163284885 | 1.618034 |
| 116 | 781774079430987230203437 | 1.618034 |
| 117 | 1264937032042997393488322 | 1.618034 |
| 118 | 2046711111473984623691759 | 1.618034 |
| 119 | 3311648143516982017180081 | 1.618034 |
| 120 | 5358359254990966640871840 | 1.618034 |
| 121 | 8670007398507948658051921 | 1.618034 |
| 122 | 14028366653498915298923761 | 1.618034 |
| 123 | 22698374052006863956975682 | 1.618034 |
| 124 | 36726740705505779255899443 | 1.618034 |
| 125 | 59425114757512643212875125 | 1.618034 |
| 126 | 96151855463018422468774568 | 1.618034 |
| 127 | 155576970220531065681649693 | 1.618034 |
| 128 | 251728825683549488150424261 | 1.618034 |
| 129 | 407305795904080553832073954 | 1.618034 |
| 130 | 659034621587630041982498215 | 1.618034 |
| 131 | 1066340417491710595814572169 | 1.618034 |
| 132 | 1725375039079340637797070384 | 1.618034 |
| 133 | 2791715456571051233611642553 | 1.618034 |
| 134 | 4517090495650391871408712937 | 1.618034 |
| 135 | 7308805952221443105020355490 | 1.618034 |
| 136 | 11825896447871834976429068427 | 1.618034 |
| 137 | 19134702400093278081449423917 | 1.618034 |
| 138 | 30960598847965113057878492344 | 1.618034 |
| 139 | 50095301248058391139327916261 | 1.618034 |
| 140 | 81055900096023504197206408605 | 1.618034 |
| 141 | 131151201344081895336534324866 | 1.618034 |
| 142 | 212207101440105399533740733471 | 1.618034 |
| 143 | 343358302784187294870275058337 | 1.618034 |
| 144 | 555565404224292694404015791808 | 1.618034 |
| 145 | 898923707008479989274290850145 | 1.618034 |
| 146 | 1454489111232772683678306641953 | 1.618034 |
| 147 | 2353412818241252672952597492098 | 1.618034 |
| 148 | 3807901929474025356630904134051 | 1.618034 |
| 149 | 6161314747715278029583501626149 | 1.618034 |
| 150 | 9969216677189303386214405760200 | 1.618034 |
| 151 | 16130531424904581415797907386349 | 1.618034 |
| 152 | 26099748102093884802012313146549 | 1.618034 |
| 153 | 42230279526998466217810220532898 | 1.618034 |
| 154 | 68330027629092351019822533679447 | 1.618034 |
| 155 | 110560307156090817237632754212345 | 1.618034 |
| 156 | 178890334785183168257455287891792 | 1.618034 |
| 157 | 289450641941273985495088042104137 | 1.618034 |
| 158 | 468340976726457153752543329995929 | 1.618034 |
| 159 | 757791618667731139247631372100066 | 1.618034 |
| 160 | 1226132595394188293000174702095995 | 1.618034 |
| 161 | 1983924214061919432247806074196061 | 1.618034 |
| 162 | 3210056809456107725247980776292056 | 1.618034 |
| 163 | 5193981023518027157495786850488117 | 1.618034 |
| 164 | 8404037832974134882743767626780173 | 1.618034 |
| 165 | 13598018856492162040239554477268290 | 1.618034 |
| 166 | 22002056689466296922983322104048463 | 1.618034 |
| 167 | 35600075545958458963222876581316753 | 1.618034 |
| 168 | 57602132235424755886206198685365216 | 1.618034 |
| 169 | 93202207781383214849429075266681969 | 1.618034 |
| 170 | 150804340016807970735635273952047185 | 1.618034 |
| 171 | 244006547798191185585064349218729154 | 1.618034 |
| 172 | 394810887814999156320699623170776339 | 1.618034 |
| 173 | 638817435613190341905763972389505493 | 1.618034 |
| 174 | 1033628323428189498226463595560281832 | 1.618034 |
| 175 | 1672445759041379840132227567949787325 | 1.618034 |
| 176 | 2706074082469569338358691163510069157 | 1.618034 |
| 177 | 4378519841510949178490918731459856482 | 1.618034 |
| 178 | 7084593923980518516849609894969925639 | 1.618034 |
| 179 | 11463113765491467695340528626429782121 | 1.618034 |
| 180 | 18547707689471986212190138521399707760 | 1.618034 |
| 181 | 30010821454963453907530667147829489881 | 1.618034 |
| 182 | 48558529144435440119720805669229197641 | 1.618034 |
| 183 | 78569350599398894027251472817058687522 | 1.618034 |
| 184 | 127127879743834334146972278486287885163 | 1.618034 |
| 185 | 205697230343233228174223751303346572685 | 1.618034 |
| 186 | 332825110087067562321196029789634457848 | 1.618034 |
| 187 | 538522340430300790495419781092981030533 | 1.618034 |
| 188 | 871347450517368352816615810882615488381 | 1.618034 |
| 189 | 1409869790947669143312035591975596518914 | 1.618034 |
| 190 | 2281217241465037496128651402858212007295 | 1.618034 |
| 191 | 3691087032412706639440686994833808526209 | 1.618034 |
| 192 | 5972304273877744135569338397692020533504 | 1.618034 |
| 193 | 9663391306290450775010025392525829059713 | 1.618034 |
| 194 | 15635695580168194910579363790217849593217 | 1.618034 |
| 195 | 25299086886458645685589389182743678652930 | 1.618034 |
| 196 | 40934782466626840596168752972961528246147 | 1.618034 |
| 197 | 66233869353085486281758142155705206899077 | 1.618034 |
| 198 | 107168651819712326877926895128666735145224 | 1.618034 |
| 199 | 173402521172797813159685037284371942044301 | 1.618034 |
| 200 | 280571172992510140037611932413038677189525 | 1.618034 |
| 201 | 453973694165307953197296969697410619233826 | 1.618034 |
| 202 | 734544867157818093234908902110449296423351 | 1.618034 |
| 203 | 1188518561323126046432205871807859915657177 | 1.618034 |
| 204 | 1923063428480944139667114773918309212080528 | 1.618034 |
| 205 | 3111581989804070186099320645726169127737705 | 1.618034 |
| 206 | 5034645418285014325766435419644478339818233 | 1.618034 |
| 207 | 8146227408089084511865756065370647467555938 | 1.618034 |
| 208 | 13180872826374098837632191485015125807374171 | 1.618034 |
| 209 | 21327100234463183349497947550385773274930109 | 1.618034 |
| 210 | 34507973060837282187130139035400899082304280 | 1.618034 |
| 211 | 55835073295300465536628086585786672357234389 | 1.618034 |