Module integer_sequences.sequences
Expand source code
EXAMPLE_LOG_AS_INTS = [
(1, 2, 3, 4),
(1, 3, 2, 4),
]
"""An example XES trace converted to integers."""
FIB = [
1,
1,
2,
3,
5,
8,
13,
21,
34,
55,
89,
144,
233,
377,
610,
987,
1597,
2584,
4181,
6765,
10946,
17711,
28657,
46368,
75025,
121393,
196418,
317811,
514229,
832040,
1346269,
2178309,
3524578,
5702887,
9227465,
14930352,
24157817,
39088169,
63245986,
102334155,
165580141,
267914296,
433494437,
701408733,
1134903170,
1836311903,
2971215073,
4807526976,
7778742049,
12586269025,
20365011074,
32951280099,
53316291173,
86267571272,
139583862445,
225851433717,
365435296162,
591286729879,
956722026041,
1548008755920,
2504730781961,
4052739537881,
6557470319842,
10610209857723,
17167680177565,
27777890035288,
44945570212853,
72723460248141,
117669030460994,
190392490709135,
308061521170129,
498454011879264,
806515533049393,
1304969544928657,
2111485077978050,
3416454622906707,
5527939700884757,
8944394323791464,
14472334024676221,
23416728348467685,
37889062373143906,
61305790721611591,
99194853094755497,
160500643816367088,
259695496911122585,
420196140727489673,
679891637638612258,
1100087778366101931,
1779979416004714189,
2880067194370816120,
4660046610375530309,
7540113804746346429,
12200160415121876738,
19740274219868223167,
31940434634990099905,
51680708854858323072,
83621143489848422977,
135301852344706746049,
218922995834555169026,
354224848179261915075,
]
"""First 100 digits in the fibonacci sequence."""
PASCAL = [
1,
1,
1,
1,
2,
1,
1,
3,
3,
1,
1,
4,
6,
4,
1,
1,
5,
10,
10,
5,
1,
1,
6,
15,
20,
15,
6,
1,
1,
7,
21,
35,
35,
21,
7,
1,
1,
8,
28,
56,
70,
56,
28,
8,
1,
1,
9,
36,
84,
126,
126,
84,
36,
9,
1,
1,
10,
45,
120,
210,
252,
210,
120,
45,
10,
1,
1,
11,
55,
165,
330,
462,
462,
330,
165,
55,
11,
1,
1,
12,
66,
220,
495,
792,
924,
792,
495,
220,
66,
12,
1,
1,
13,
78,
286,
715,
1287,
1716,
1716,
1287,
]
"""First 100 digits in the sequence given by the triangle of pascal."""
CATALAN = [
1,
1,
2,
5,
14,
42,
132,
429,
1430,
4862,
16796,
58786,
208012,
742900,
2674440,
9694845,
35357670,
129644790,
477638700,
1767263190,
6564120420,
24466267020,
91482563640,
343059613650,
1289904147324,
4861946401452,
18367353072152,
69533550916004,
263747951750360,
1002242216651368,
3814986502092304,
14544636039226909,
55534064877048198,
212336130412243110,
812944042149730764,
3116285494907301262,
11959798385860453492,
45950804324621742364,
176733862787006701400,
680425371729975800390,
2622127042276492108820,
10113918591637898134020,
39044429911904443959240,
150853479205085351660700,
583300119592996693088040,
2257117854077248073253720,
8740328711533173390046320,
33868773757191046886429490,
131327898242169365477991900,
509552245179617138054608572,
1978261657756160653623774456,
7684785670514316385230816156,
29869166945772625950142417512,
116157871455782434250553845880,
451959718027953471447609509424,
1759414616608818870992479875972,
6852456927844873497549658464312,
26700952856774851904245220912664,
104088460289122304033498318812080,
405944995127576985730643443367112,
1583850964596120042686772779038896,
6182127958584855650487080847216336,
24139737743045626825711458546273312,
94295850558771979787935384946380125,
368479169875816659479009042713546950,
1440418573150919668872489894243865350,
5632681584560312734993915705849145100,
22033725021956517463358552614056949950,
86218923998960285726185640663701108500,
337485502510215975556783793455058624700,
1321422108420282270489942177190229544600,
5175569924646105559418940193995065716350,
20276890389709399862928998568254641025700,
79463489365077377841208237632349268884500,
311496878311103321137536291518809134027240,
1221395654430378811828760722007962130791020,
4790408930363303911328386208394864461024520,
18793142726809884575211361279087545193250040,
73745243611532458459690151854647329239335600,
289450081175264899454283846029490767264392230,
1136359577947336271931632877004667456667613940,
4462290049988320482463241297506133183499654740,
17526585015616776834735140517915655636396234280,
68854441132780194707888052034668647142985206100,
270557451039395118028642463289168566420671280440,
1063353702922273835973036658043476458723103404520,
4180080073556524734514695828170907458428751314320,
16435314834665426797069144960762886143367590394940,
64633260585762914370496637486146181462681535261000,
254224158304000796523953440778841647086547372026600,
1000134600800354781929399250536541864362461089950800,
3935312233584004685417853572763349509774031680023800,
15487357822491889407128326963778343232013931127835600,
60960876535340415751462563580829648891969728907438000,
239993345518077005168915776623476723006280827488229600,
944973797977428207852605870454939596837230758234904050,
3721443204405954385563870541379246659709506697378694300,
14657929356129575437016877846657032761712954950899755100,
57743358069601357782187700608042856334020731624756611000,
227508830794229349661819540395688853956041682601541047340,
896519947090131496687170070074100632420837521538745909320,
]
"""First 100 catalan numbers."""
RECAMAN = [
0,
1,
3,
6,
2,
7,
13,
20,
12,
21,
11,
22,
10,
23,
9,
24,
8,
25,
43,
62,
42,
63,
41,
18,
42,
17,
43,
16,
44,
15,
45,
14,
46,
79,
113,
78,
114,
77,
39,
78,
38,
79,
37,
80,
36,
81,
35,
82,
34,
83,
33,
84,
32,
85,
31,
86,
30,
87,
29,
88,
28,
89,
27,
90,
26,
91,
157,
224,
156,
225,
155,
226,
154,
227,
153,
228,
152,
75,
153,
74,
154,
73,
155,
72,
156,
71,
157,
70,
158,
69,
159,
68,
160,
67,
161,
66,
162,
65,
163,
64,
]
"""First 100 digits in the recaman sequence."""
UP = [
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40,
41,
42,
43,
44,
45,
46,
47,
48,
49,
50,
51,
52,
53,
54,
55,
56,
57,
58,
59,
60,
61,
62,
63,
64,
65,
66,
67,
68,
69,
70,
71,
72,
73,
74,
75,
76,
77,
78,
79,
80,
81,
82,
83,
84,
85,
86,
87,
88,
89,
90,
91,
92,
93,
94,
95,
96,
97,
98,
99,
100,
]
"""First 100 digits in the sequence as generated by `range_up`, with sane defaults.
Created with Excel, so this testcase assumes correctness of Excel."""
DOWN = [
100,
99,
98,
97,
96,
95,
94,
93,
92,
91,
90,
89,
88,
87,
86,
85,
84,
83,
82,
81,
80,
79,
78,
77,
76,
75,
74,
73,
72,
71,
70,
69,
68,
67,
66,
65,
64,
63,
62,
61,
60,
59,
58,
57,
56,
55,
54,
53,
52,
51,
50,
49,
48,
47,
46,
45,
44,
43,
42,
41,
40,
39,
38,
37,
36,
35,
34,
33,
32,
31,
30,
29,
28,
27,
26,
25,
24,
23,
22,
21,
20,
19,
18,
17,
16,
15,
14,
13,
12,
11,
10,
9,
8,
7,
6,
5,
4,
3,
2,
1,
]
"""First 100 digits in the sequence as generated by `range_down`, with sane defaults.
Created with Excel, so this testcase assumes correctness of Excel."""
LONGTERM = [
1,
2,
3,
4,
5,
6,
8,
11,
15,
20,
26,
34,
45,
60,
80,
106,
140,
185,
245,
325,
431,
571,
756,
1001,
1326,
1757,
2328,
3084,
4085,
5411,
7168,
9496,
12580,
16665,
22076,
29244,
38740,
51320,
67985,
90061,
119305,
158045,
209365,
277350,
367411,
486716,
644761,
854126,
1131476,
1498887,
1985603,
2630364,
3484490,
4615966,
6114853,
8100456,
10730820,
14215310,
18831276,
24946129,
33046585,
43777405,
57992715,
76823991,
101770120,
134816705,
178594110,
236586825,
313410816,
415180936,
549997641,
728591751,
965178576,
1278589392,
1693770328,
2243767969,
2972359720,
3937538296,
5216127688,
6909898016,
9153665985,
12126025705,
16063564001,
21279691689,
28189589705,
37343255690,
49469281395,
65532845396,
86812537085,
115002126790,
152345382480,
201814663875,
267347509271,
354160046356,
469162173146,
621507555626,
823322219501,
1090669728772,
1444829775128,
1913991948274,
]
"""First 100 digits in the long_term_dependency sequence, with sane defaults.
Created with Excel, so this testcase assumes correctness of Excel."""
LONGTERM_SINGLE = [
1,
2,
3,
4,
5,
5,
10,
15,
20,
25,
25,
50,
75,
100,
125,
125,
250,
375,
500,
625,
625,
1250,
1875,
2500,
3125,
3125,
6250,
9375,
12500,
15625,
15625,
31250,
46875,
62500,
78125,
78125,
156250,
234375,
312500,
390625,
390625,
781250,
1171875,
1562500,
1953125,
1953125,
3906250,
5859375,
7812500,
9765625,
9765625,
19531250,
29296875,
39062500,
48828125,
48828125,
97656250,
146484375,
195312500,
244140625,
244140625,
488281250,
732421875,
976562500,
1220703125,
1220703125,
2441406250,
3662109375,
4882812500,
6103515625,
6103515625,
12207031250,
18310546875,
24414062500,
30517578125,
30517578125,
61035156250,
91552734375,
122070312500,
152587890625,
152587890625,
305175781250,
457763671875,
610351562500,
762939453125,
762939453125,
1525878906250,
2288818359375,
3051757812500,
3814697265625,
3814697265625,
7629394531250,
11444091796875,
15258789062500,
19073486328125,
19073486328125,
38146972656250,
57220458984375,
76293945312500,
95367431640625,
]
"""First 100 digits in the long_term_single_dependency sequence, with sane defaults.
Created with Excel, so this testcase assumes correctness of Excel"""
SHORTTERM_SINGLE = [
1,
7,
49,
343,
2401,
16807,
117649,
823543,
5764801,
40353607,
282475249,
1977326743,
13841287201,
96889010407,
678223072849,
4747561509943,
33232930569601,
232630513987207,
1628413597910449,
11398895185373143,
79792266297612001,
558545864083284007,
3909821048582988049,
27368747340080916343,
191581231380566414401,
1341068619663964900807,
9387480337647754305649,
65712362363534280139543,
459986536544739960976801,
3219905755813179726837607,
22539340290692258087863249,
157775382034845806615042743,
1104427674243920646305299201,
7730993719707444524137094407,
54116956037952111668959660849,
378818692265664781682717625943,
2651730845859653471779023381601,
18562115921017574302453163671207,
129934811447123020117172145698449,
909543680129861140820205019889143,
6366805760909027985741435139224001,
44567640326363195900190045974568007,
311973482284542371301330321821976049,
2183814375991796599109312252753832343,
15286700631942576193765185769276826401,
107006904423598033356356300384937784807,
749048330965186233494494102694564493649,
5243338316756303634461458718861951455543,
36703368217294125441230211032033660188801,
256923577521058878088611477224235621321607,
1798465042647412146620280340569649349251249,
12589255298531885026341962383987545444758743,
88124787089723195184393736687912818113311201,
616873509628062366290756156815389726793178407,
4318114567396436564035293097707728087552248849,
30226801971775055948247051683954096612865741943,
211587613802425391637729361787678676290060193601,
1481113296616977741464105532513750734030421355207,
10367793076318844190248738727596255138212949486449,
72574551534231909331741171093173785967490646405143,
508021860739623365322188197652216501772434524836001,
3556153025177363557255317383565515512407041673852007,
24893071176241544900787221684958608586849291716964049,
174251498233690814305510551794710260107945042018748343,
1219760487635835700138573862562971820755615294131238401,
8538323413450849900970017037940802745289307058918668807,
59768263894155949306790119265585619217025149412430681649,
418377847259091645147530834859099334519176045887014771543,
2928644930813641516032715844013695341634232321209103400801,
20500514515695490612229010908095867391439626248463723805607,
143503601609868434285603076356671071740077383739246066639249,
1004525211269079039999221534496697502180541686174722466474743,
7031676478883553279994550741476882515263791803223057265323201,
49221735352184872959961855190338177606846542622561400857262407,
344552147465294110719732986332367243247925798357929806000836849,
2411865032257058775038130904326570702735480588505508642005857943,
16883055225799411425266916330285994919148364119538560494041005601,
118181386580595879976868414312001964434038548836769923458287039207,
827269706064171159838078900184013751038269841857389464208009274449,
5790887942449198118866552301288096257267888893001726249456064921143,
40536215597144386832065866109016673800875222251012083746192454448001,
283753509180010707824461062763116716606126555757084586223347181136007,
1986274564260074954771227439341817016242885890299592103563430267952049,
13903921949820524683398592075392719113700201232097144724944011875664343,
97327453648743672783790144527749033795901408624680013074608083129650401,
681292175541205709486531011694243236571309860372760091522256581907552807,
4769045228788439966405717081859702655999169022609320640655796073352869649,
33383316601519079764840019573017918591994183158265244484590572513470087543,
233683216210633558353880137011125430143959282107856711392134007594290612801,
1635782513474434908477160959077878011007714974754996979744938053160034289607,
11450477594321044359340126713545146077054004823284978858214566372120240027249,
80153343160247310515380886994816022539378033762994852007501964604841680190743,
561073402121731173607666208963712157775646236340963964052513752233891761335201,
3927513814852118215253663462745985104429523654386747748367596265637242329346407,
27492596703964827506775644239221895731006665580707234238573173859460696305424849,
192448176927753792547429509674553270117046659064950639670012217016224874137973943,
1347137238494276547832006567721872890819326613454654477690085519113574118965817601,
9429960669459935834824045974053110235735286294182581343830598633795018832760723207,
66009724686219550843768321818371771650147004059278069406814190436565131829325062449,
462068072803536855906378252728602401551029028414946485847699333055955922805275437143,
]
"""First 100 digits in the short_term_single_dependency sequence, with constant being 7.
Cannot be recreated with Excel due to precision issues - coded up instead."""Global variables
var CATALAN-
First 100 catalan numbers.
var DOWN-
First 100 digits in the sequence as generated by
range_down, with sane defaults. Created with Excel, so this testcase assumes correctness of Excel. var EXAMPLE_LOG_AS_INTS-
An example XES trace converted to integers.
var FIB-
First 100 digits in the fibonacci sequence.
var LONGTERM-
First 100 digits in the long_term_dependency sequence, with sane defaults. Created with Excel, so this testcase assumes correctness of Excel.
var LONGTERM_SINGLE-
First 100 digits in the long_term_single_dependency sequence, with sane defaults. Created with Excel, so this testcase assumes correctness of Excel
var PASCAL-
First 100 digits in the sequence given by the triangle of pascal.
var RECAMAN-
First 100 digits in the recaman sequence.
var SHORTTERM_SINGLE-
First 100 digits in the short_term_single_dependency sequence, with constant being 7. Cannot be recreated with Excel due to precision issues - coded up instead.
var UP-
First 100 digits in the sequence as generated by
range_up, with sane defaults. Created with Excel, so this testcase assumes correctness of Excel.