4-ary Boolean functions; clans in rational order

Compare 4-ary Boolean functions#Big equivalence classes (bec)

In this table the Boolean functions are sorted as fractions in colex order.
This order is independent of arity (unlike that of integers in A227723).
The number of BECs by actual arity is found in A000618. (Compare A000616 for acual or smaller arity.)

        n        0,  1,  2,   3,    4        arity
      2^n        1,  2,  4,   8,   16        period length
A000618(n)       2,  1,  3,  16,  380        number of BECs of arity = n
A000616(n)       2,  3,  6,  22,  402        number of BECs of arity ≤ n

The same information in a Python dict: https://pastebin.com/q2d4aWVE
Map from the 65536 functions to the BEC index numbers: https://pastebin.com/3fBShT7M
The 168 monotonic functions belonging to 30 BECs: https://pastebin.com/JUeKsasG

I accidentally reflected the period in the table below. E.g. 1/3 in binary is .0101... - not .1010. I will fix it later.

c a weight so
na
no
mo
rational number value f/s
 
s/b
ary
f/b
ary
s/b f/b
num over den period num den dec 0 1 2 3 4 0 1 2 3 4
 
0100/1000000000000000000010.0000001111111111111
1001/116s01111111111111111111.0000001111111111111
211/28s01010101010101010130.33333321212342468
321/28s40110011001100110250.4000002121362612
4521/44s010001000100010001150.06666741413641224
5423/412011101110111011107150.46666741413641224
631/28201111000011110002170.11764783243122496
731/28s410010110100101107170.4117652121428
81331/44s200101000001010004510.07843143123121248
91233/86210011000100110005510.09803983243122496
101133/86011000100110001007510.13725583243122496
111035/8100111011001110110011510.21568683243122496
12935/8102011101100111011022510.43137383243122496
13833/4122101111101011111025510.49019643123121248
141631/44s200011000000110008850.09411841414416
1531/28211011000110110009850.10588283243122496
161433/4122011111100111111042850.49411841414416
172131/82s0100000001000000012550.00392281814832
182033/8620110100001101000222550.08627581814832
1931/2801110100011101000232550.09019681814832
201835/810211010110110101101072550.41960881814832
211737/814011111110111111101272550.49803981814832
2241/281011111111000000022570.00778216464464
2341/283100111110110000072570.027237812961296
2441/283000111111110000082570.031128161219212192
2541/2841001011101101000232570.08949416464464
2641/2840001011111101000242570.0933858432432
2741/2821110011100011000252570.0972768432432
2841/2830110011110011000262570.101167161219212192
2941/2840010011111011000282570.108949812961296
3041/2841000011101111000312570.1206238648648
3141/28s501101001100101101062570.41245121212
329541/441001010101000000047710.005188161219212192
339445/1652100101011000000057710.006485161219212192
3410945/1652110010100100000077710.009079161219212192
359647/16711110010111000000117710.014267162438424384
364447/16711111001001100000197710.024643161219212192
379745/16530010010101100000207710.025940161219212192
386747/16720111001011100000227710.028534161219212192
399847/16721100010111100000237710.029831161219212192
407845/16511011001000010000257710.032425161219212192
418245/16520011001010010000287710.036316162438424384
429143/8611101001001010000317710.040208162438424384
439343/8610101001011010000347710.044099161219212192
443649/16911111100111010000357710.045396161219212192
459045/16511001001000110000377710.04799016696696
465747/16710111100100110000387710.049287161219212192
476541/2811011100110110000417710.053178161219212192
487247/16720011100101110000447710.057069162438424384
495047/16720110001011110000467710.059663161219212192
504949/16921101100111110000477710.060960161219212192
5111045/16521100001001001000557710.071336162438424384
5211145/16520100001011001000587710.075227162438424384
539941/2811110100111001000597710.076524161219212192
5410741/44s21000001000101000617710.0791184416416
5510043/8630110100100101000627710.080415812961296
5610147/16711010100110101000657710.084306161219212192
574649/16911111110001101000677710.086900161219212192
5810243/8630010100101101000687710.088197812961296
596949/16910111110011101000707710.09079116696696
6010341/2811100100111101000717710.092088161219212192
617947/16731011110000011000737710.094682162438424384
6210445/16530100100100011000747710.095979161219212192
638747/16730011110010011000767710.098573162438424384
6410543/8621000100110011000777710.0998708648648
654741/2811101110001011000797710.102464161219212192
667141/2820101110011011000827710.106355161219212192
673849/16921111000111011000837710.107652161219212192
688947/16731001110000111000857710.110246161219212192
695947/16710111000100111000867710.11154316696696
708147/16740001110010111000887710.114137161219212192
716641/2821011000110111000897710.115435161219212192
724849/16921110110001111000917710.118029162438424384
738643/86101001100110001001067710.137484812961296
7410647/167211100001110001001077710.138781161219212192
758043/86210110100000101001217710.156939162438424384
768843/86300110100100101001247710.160830162438424384
779247/167011010100010101001277710.164721161219212192
7840411/1611111111110110101001317710.169909161219212192
796149/169301111110001101001347710.173800162438424384
807545/810210111110101101001377710.177691162438424384
817049/169400111110011101001407710.181582161219212192
8241411/1611211011110111101001437710.185473162438424384
8341/28201101110001011001587710.204929162438424384
8410849/169110101110101011001617710.208820162438424384
8541/28300101110011011001647710.212711162438424384
867345/810111001110111011001677710.216602812961296
876349/169301110110001111001827710.236057162438424384
887645/810310110110101111001857710.239948162438424384
896849/169300110110011111001887710.243839161219212192
9045411/1611111010110111111001917710.24773016696696
914245/810111111010110100102277710.294423162438424384
927749/169010111010101100102337710.302205161219212192
934345/810111011010111100102397710.309987161219212192
9433411/1611201111111011010102627710.339818161219212192
953243/412110111111111010102657710.343709161219212192
963549/169100111111000110102687710.347601162438424384
9737411/1611310011111110110102777710.359274161219212192
983949/169200011111001110102807710.363165161219212192
995341/28100110111000101103167710.409857161219212192
1005545/810311010111100101103197710.413748812961296
1015649/169101010111010101103227710.417639161219212192
1025845/810310010111110101103257710.421530812961296
1036041/28100010111001101103287710.425422161219212192
10462411/1611311100111101101103317710.429313161219212192
1056445/810201100111011101103347710.4332048648648
1067449/169200111011000111103647710.472114161219212192
1075443/412211101011101111103797710.4915694416416
1088447/167101010011010100014187710.542153162438424384
10934411/1611210111111001101015217710.675746161219212192
11051411/1611210110111001111015697710.738003162438424384
11152411/1611200110111101111015727710.741894162438424384
11218041/4420001100110000000812850.006226161219212192
11314843/8621101001110000000912850.007004162438424384
11418143/86211101001010000001312850.010117161219212192
11518243/86201101001110000001812850.014008161219212192
11617143/86310010011110000001912850.014786161219212192
11713043/86111110100001000002112850.01634216696696
11816643/86210110100011000003112850.024125161219212192
11918541/44s300000110011000003212850.0249034312312
12018443/86311001001011000003312850.025681161219212192
12115443/86200110100111000003612850.028016161219212192
12217643/86301001001111000003812850.029572162438424384
12314443/86201111010000100004212850.032685162438424384
12417343/86300111010010100005212850.040467161219212192
12541/28211011010110100005712850.044358162438424384
12617743/86310000011110100005912850.045914161219212192
12715843/86110110001001100006312850.049027161219212192
12816843/86201100100101100006612850.05136216464464
12915147/167110011010101100006712850.052140161219212192
13011745/810111111101101100006912850.05369616696696
13115343/86200011010011100007212850.056031161219212192
13215247/167111010001011100007312850.056809161219212192
13314341/28210011101110010009912850.077043162438424384
13418645/1652010010100010100010212850.079377161219212192
13517443/863000111010010100010412850.080934161219212192
13616747/1672101110000110100011112850.086381162438424384
13718743/862110000010110100011312850.08793816696696
13841/283011011010110100011412850.088716161219212192
13914147/1672001110001110100011612850.090272162438424384
14014543/862010000011110100011812850.091829161219212192
14113949/1692101011011110100011912850.092607162438424384
14218841/44s3100000010001100012312850.0957204624624
14313341/282110011011001100012912850.100389162438424384
14412345/8102111111100101100013312850.103502162438424384
14514045/8102011111101101100013812850.107393161219212192
14641/283100011011101100013912850.108171812961296
14716049/1692101111100011100014312850.11128416696696
14811345/8102111101011011100014912850.115953162438424384
14915043/862000100100111100015212850.118288161219212192
15014945/8102110111100111100015312850.119066161219212192
15112949/1691011101010111100015412850.119844161219212192
15213249/1691111000101111100015712850.122179161219212192
15313145/8102010111101111100015812850.122957161219212192
15412145/8102101101011111100015912850.123735161219212192
15518947/1673001011101010010018812850.146304162438424384
15641/283111001011010010018912850.147082161219212192
15717847/1672011001010110010019412850.150973162438424384
15812745/8101111111001110010019712850.153307161219212192
15941/283101001011110010019912850.154864162438424384
16014747/1672011111000001010020212850.15719816696696
16116341/282101111001001010020712850.161089161219212192
16217547/1672001111000101010021212850.164981161219212192
16316141/282101101100011010022312850.173541161219212192
16416541/283100111001011010022712850.176654161219212192
16516441/283001101101011010022812850.177432161219212192
16611845/8102111110011011010022912850.178210161219212192
16713649/1692110101100111010023312850.181323162438424384
16812845/8102101110011111010023912850.18599216464464
16919047/1672101001100010110026312850.204669161219212192
17017943/863000110010010110026412850.205447161219212192
17111645/8103001111110110110027612850.214786161219212192
17218343/863001010010001110028412850.221012161219212192
17312445/8103111110100101110029312850.228016161219212192
17413545/8103011110101101110029812850.231907161219212192
17516249/1692101110100011110030312850.235798161219212192
17612245/8103110110100111110031312850.243580162438424384
17712645/8103001011110111110031612850.245914161219212192
17815749/1692011011100110101043412850.337743162438424384
17917045/8103110100111110011052112850.405447161219212192
18011243/4122011111111110011052212850.406226161219212192
18111445/8102101111110001011052712850.410117161219212192
18211545/8102001111111001011053212850.414008161219212192
18317245/8103111000111101011054112850.421012161219212192
18412045/8103100111110011011054712850.425681161219212192
18511943/4123011011111111011056212850.4373544312312
186134411/16112110101110101111061712850.480156161219212192
18713745/8102100101110011111062712850.48793816696696
18814243/4123111001110111111063712850.4957204624624
18915549/1693010110111101000170212850.546304162438424384
19016949/1692110100110101100177712850.604669161219212192
19129041/82s100001000100000001638550.0041508648648
19228543/163110000100100000001738550.004410161219212192
19329141/44111000010100000001938550.00492916696696
19423643/86101101110100000002238550.005707161219212192
19528645/165111100001100000002338550.005966161219212192
19622045/165011110000010000003138550.008042161219212192
19729243/163101000010010000003438550.00882016464464
19828741/44201100001010000003838550.009857161219212192
19924745/165101110000110000004638550.011933161219212192
20028141/44110000010110000004938550.012711161219212192
20126041/44010110000001000006138550.01582416464464
20227141/44100110000101000007638550.019715161219212192
20341/28011111100101000007938550.020493161219212192
20427745/165111010000011000009138550.02360616464464
20528841/44201000001011000009838550.025422161219212192
20623947/1673101011010110000010138550.026200162438424384
20741/282111010110110000010338550.026719162438424384
20824843/863000011101110000011238550.0290538648648
20928945/1651100000011110000011338550.02931316464464
21023741/282011010111110000011838550.030610162438424384
21126745/1652001111000001000012438550.032166161219212192
21223547/1672011101101001000014238550.036835161219212192
21328241/441000110000101000015238550.03942916696696
21428043/861010111000101000015438550.039948161219212192
21527045/1652000111000011000018438550.047730161219212192
21626447/1672001111100011000018838550.048768162438424384
21724647/1673100101100111000021738550.056291161219212192
21821947/1672000101101111000023238550.060182161219212192
21921849/1692100111101111000023338550.060441161219212192
220196411/16110111110111111000023938550.061997161219212192
22124347/1673110100110100100028338550.073411162438424384
22224947/1672001110110100100028438550.073671161219212192
22341/281101011101100100029338550.076005162438424384
22428443/863100001100110100033738550.0874198648648
22527947/1673101001010110100034138550.088457161219212192
22641/283111000110110100034338550.088975162438424384
22725347/1673000110110110100034438550.089235161219212192
22841/282101101001110100034938550.090532162438424384
22941/282100011101110100035338550.0915698648648
23025647/1673001001011110100035638550.092348161219212192
23141/283011000111110100035838550.092866162438424384
23225445/8101111010111110100035938550.093126161219212192
23326845/1652001101000001100036438550.09442316696696
23424147/1673011010110001100037438550.097017161219212192
23521249/1692111101101001100038338550.099351161219212192
23619445/8101111011111001100039138550.101427161219212192
23721041/282011101100101100039838550.103243162438424384
23825947/1673110000110101100040338550.104540162438424384
23920649/1693011011110101100040638550.105318162438424384
24026641/283001110101101100041238550.10687416696696
24123449/1693101101101101100041338550.107134161219212192
24226945/1652000101000011100042438550.10998716696696
24322149/1693011110011011100044638550.115694162438424384
24424541/283100110100111100045738550.11854716696696
24524441/283010101100111100045838550.11880716696696
24621749/1693100101101111100047338550.122698161219212192
247199411/16111111100111111100047938550.124254161219212192
24820845/8103100011111111100048138550.1247738648648
24922249/1692101101111100010054138550.140337161219212192
25027347/1672100111010010010055338550.143450161219212192
25128347/1673011010011010010056638550.14682216696696
25226347/1672100100111010010056938550.14760116348348
25322749/1693100101111110010060138550.155901161219212192
25423243/861000101110001010061638550.159792161219212192
25527647/1673001011011001010062838550.16290516464464
25623049/1693101001111101010066138550.171466161219212192
25725847/1672110100100011010066738550.173022161219212192
25825749/1692110110101011010068338550.177173161219212192
25923849/1693110001111011010069138550.179248162438424384
26020143/4120111111011111010071938550.18651116464464
26127241/281010111010010110079438550.20596616348348
26241/282110010101010110080338550.2083018648648
26325249/1692010110110110110082638550.21426716348348
26421649/1692111111000001110084738550.219715162438424384
26527541/282011011010001110085438550.22153016696696
26624041/283011100100101110087838550.22775616696696
267211411/16112111111100011110091138550.236316161219212192
268233411/16112011111101011110092638550.24020816696696
269242411/16112101111100111110094138550.24409916696696
270215411/16112001111101111110095638550.247990161219212192
27120243/4121111101011111110095938550.248768161219212192
27226141/2811101001110100010105138550.27263316348348
27325049/16921101101101100010106738550.276783161219212192
27441/2830110100111100010107838550.279637162438424384
27526541/2821110001110010010111138550.28819716696696
27625549/16930110101111010010114238550.29623916464464
277204411/161111111100111110010119938550.31102516464464
27841/2821110000101101010130338550.338003161219212192
27922549/16930110110101011010136638550.354345161219212192
28021445/81011111101000111010139138550.360830161219212192
28120043/41211111111001111010142338550.369131161219212192
28221343/41210111111011111010143838550.37302216696696
28325149/16931110010110010110159138550.41271116696696
28422445/81030110110111010110162238550.4207528648648
285192413/161311111111011110110167938550.435538161219212192
286195411/161110111111100011110182238550.472633161219212192
28719843/41221011111110011110183738550.476524161219212192
28820543/41221001111110111110189738550.492088161219212192
289209411/161110001111101111110191238550.49597916464464
29019147/81411110111111111110192738550.4998708648648
29119343/41210111111100111101284638550.73826216696696
292197413/161311011111110111101286138550.74215316464464
29332341/44200010110100000002443690.00549316464464
29432241/44201100001100000002643690.00595116696696
29541/28111110111100000003343690.007553161219212192
29630545/165011010100010000003743690.00846916116116
29731247/167011101010110000005743690.01304616348348
29830341/282101111010110000011543690.026322161219212192
29931347/1671111001101000100029743690.06797916464464
30031843/862110010010100100031743690.072557161219212192
30132143/861001010101010100036443690.0833148432432
30231547/1672100011100110100038343690.08766316696696
30329841/282111100010110100038543690.088121161219212192
30430941/283001111010110100038843690.088808161219212192
305296411/16110111111101110100040143690.09178316116116
30641/283011100011110100040243690.092012812961296
30741/284001101011110100040443690.092470162438424384
30832047/1672100101010101100045543690.104143161219212192
30930441/283011010110101100045843690.104829161219212192
31031649/1693110010111011100050943690.116503161219212192
31141/281111011001100010060143690.137560161219212192
31229749/1690111101011100010060943690.13939116348348
31329949/1691110111010110010066143690.15129316464464
31431947/1672100101011001010071143690.162737161219212192
31530249/1692011011011101010074643690.17074816696696
31631047/1673010001110011010076643690.175326161219212192
31741/285001101011010110091643690.2096598324324
31830045/8102110110011110110094943690.217212161219212192
31931449/16920110101101101010148243690.339208161219212192
32030849/16921010011101101010148343690.339437161219212192
32130145/81011010101111101010149943690.3430998432432
32229443/41221111101111010110184143690.42137816696696
32329343/41221011111111010110184343690.42183616464464
32434943/163011000100000000007131070.00053416696696
32536043/1632000110001000000056131070.00427316696696
32636141/82s1000000101000000064131070.0048838432432
32735743/1632000010011000000080131070.00610416348348
32834845/1651001100111000000092131070.00701916696696
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