An Introduction to the Series: In Action

Here is a list of the first 200 Fibonacci numbers, just for reference.

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