Details Page for 0.3507

Complete Solution is Known:

Period:  
Preperiod:  
Quotient Size:   4804
P-Portion Size:   756
Tame?   No

MSV File: q-0.3507.msv

Growth Pattern:

Heap   Q-Size   P-Size
121
262
4144
8225
9326
139617
1420436
1538868
1649273
1761298
18764134
194804756

(Click on a heap to see details)

Details for Q19(0.3507):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n | a2=1, b3=b, b2c=c, c3=ac2, b2d=d, c2d=abc2, d2=b2, b2e=e, c2e=bc2, e2=c2, c2f=abc2, cef=c2, b2f2=f2, cf2=ac2, f3=acf, b2g=g, cg=bcde, eg=ac2, g2=c2, b2h=h, cdh=abch, cfh=aceh, defh=abefh, f2h=ach, gh=bdeh, c2h2=c2, dfh2=abfh2, ch3=ch, eh3=eh, h4=h2, b2i=i, c2i=ac2h, cdi=abci, cei=aceh, cfi=ceh, efi=aefh, gi=bdei, chi=ach2, fhi=afh2, h3i=hi, f2i2=aci2, hi2=ah2i, ci3=ci, i4=i2, b2j=j, c2j=c2h, chj=ch2, efhj=efh2, fh2j=fh3, cij=aci2, hij=h2i, fi2j=afi3, ehj2=eh2j, h2j2=h3j, eij2=ei, cej3=cej, i2j3=i2j, cfj4=cfj2, ef2j4=ef2j2, f2gj4=f2gj2, hj4=hj2, ij4=ij2, cj5=cj3, ej5=ej3, f2j5=f2j3, gj5=gj3, j6=j4, b2k=k, ck=abc2, ek=c2, fk=ac2, gk=ac2, h3k=hk, hj2k=h2jk, ij2k=ik, j5k=j3k, k2=c2, b2l=l, cl=bdf2i, f2l=abdf2i, fgl=aefl, hl=ah2, eil=aehi, dfil=abfil, i3l=il, ijl=ai2l, ej4l=ej2l, gj4l=gj2l, j5l=j3l, ikl=ahik, jkl=ahjk, dfl2=abfl2, gl2=bdel2, il2=i2l, efj2l2=efl2, j3l2=jl2, efl3=aefjl2, jl3=aj2l2, kl3=kl, l4=l2, b2m=m, c2m=bc2h, cdm=abcm, cem=bceh, cfm=abceh, efm=befh, df2m=abf2m, gm=bdem, hm=adh2, cim=abch2, eim=adehi, f2im=bch2, i3m=im, fijm=afi2m, cj2m=cm, ij2m=ai2jm, j4m=j2m, ikm=adhik, j3km=jkm, lm=dh2, cm2=bcjm, f2m2=abcjm, im2=di2m, fj2m2=fm2, fm3=adfjm2, ejm3=ejm, km3=km, m4=m2, b2n=n, c2n=abc2h, chn=abch2, dehn=abehn, efhn=abefh2, fh2n=abfh3, cin=bci2, fi2n=adfi3, cejn=abceh2, ef2jn=cfjn, f2gjn=acfjn, i2j2n=i2n, dhkn=abhkn, hikn=c2h, gln=aeln, filn=bfi2l, dkln=abkln, del2n=abel2n, fl2n=bfl3, cmn=abcjm, fimn=adfi2m, ijmn=ai2mn, dej2mn=abej2mn, dkmn=abkmn, fm2n=dfjm2, em3n=emn, cdfn2=abcfn2, f2gn2=bdef2n2, dhn2=abhn2, ehn2=abeh2n, df2in2=abf2in2, cfj2n2=aceh2, f2j2n2=acj2n2, hj2n2=h2jn2, fij2n2=fi3, hkn2=abh2kn, dln2=abln2, ej2ln2=bej2l2n, fj3ln2=afj2l2, kln2=bkl2n, el2n2=bel3n, jl2n2=aj4ln2, fj2mn2=adfjm2, j2m3n2=j2mn2, cen3=cen, fgn3=bdefn3, h2n3=abh3n2, ein3=ein, hin3=abh2in2, efj3n3=defj4n2, ikn3=ikn, iln3=bi2ln2, j3ln3=abj4ln2, l2n3=bl3n2, imn3=adi2mn2, dejmn3=abejmn3, ej3mn3=ejmn3, j3m2n3=jm2n3, jm3n3=j3mn3, cfn4=cfn2, efn4=efn2, hn4=hn2, in4=in2, cj3n4=cdj4n3, fj4n4=dfj5n3, ln4=ln2, emn4=aem2n3, fmn4=fmn2, kmn4=akm2n3, cn5=cn3, f2n5=f2n3, gn5=gn3, kn5=kn3, j2mn5=aj2m2n4, m2n5=am3n4, n6=n4>

P = {a, b2, bc, c2, abd, acd, abe, de, f, abf2, df2, bg, adg, ah, bdh, abeh, deh, bfh, adfh, ah2, bch2, dh2, abeh2, fh2, ah3, bdh3, bfh3, aci, ei, abdei, afi, dfi, f2i, abdf2i, hi, adhi, behi, h2i, abdh2i, ai2, bci2, di2, abei2, fi2, abdfi2, i3, adi3, abdei3, afi3, dfi3, aj, cj, bdj, acdj, abej, dej, abcdej, fj, acfj, adfj, bcdfj, befj, abdefj, af2j, df2j, bdef2j, bgj, adgj, afgj, dfgj, f2gj, ahj, bdhj, abehj, dehj, fhj, abdfhj, ah2j, bdh2j, abeh2j, deh2j, ah3j, bdh3j, bij, adij, afij, bdfij, bf2ij, adf2ij, ai2j, bdi2j, bi3j, adi3j, j2, bcj2, acdj2, abej2, dej2, abf2j2, df2j2, bgj2, adgj2, ahj2, bdhj2, bfhj2, adfhj2, bij2, afij2, dfij2, f2ij2, abdf2ij2, ai2j2, di2j2, i3j2, adi3j2, aj3, cj3, bdj3, acdj3, abej3, dej3, fj3, acfj3, adfj3, bcdfj3, befj3, abdefj3, af2j3, df2j3, bdef2j3, bgj3, adgj3, afgj3, dfgj3, f2gj3, ahj3, bdhj3, fhj3, abdfhj3, bij3, adij3, afij3, bdfij3, bf2ij3, adf2ij3, j4, bcj4, acdj4, abej4, dej4, abf2j4, df2j4, bgj4, adgj4, aj5, bdj5, fj5, adfj5, bh2k, abhik, bi2k, abijk, dijk, abi3jk, di3jk, l, abdl, bel, adel, abfl, dfl, aefl, bdefl, abgl, dgl, ail, dil, fil, i2l, abdi2l, abfi2l, jl, abdjl, bejl, adejl, abgjl, dgjl, j2l, abdj2l, bej2l, adej2l, abfj2l, dfj2l, aefj2l, bdefj2l, abgj2l, dgj2l, j3l, abdj3l, bej3l, adej3l, abgj3l, dgj3l, j4l, abdj4l, abfj4l, dfj4l, al2, dl2, abel2, fl2, ajl2, bdjl2, abejl2, dejl2, bfjl2, efjl2, aj2l2, bdj2l2, abej2l2, dej2l2, bkl2, l3, abdl3, bel3, adel3, abfl3, abm, cm, dm, aem, bdem, fm, adfm, af2m, im, adim, abfim, dfim, ai2m, di2m, fi2m, adfi2m, abjm, cjm, djm, aejm, bdejm, bfjm, adfjm, af2jm, bijm, adijm, ai2jm, di2jm, abj2m, dj2m, aej2m, bdej2m, fj2m, adfj2m, af2j2m, abj3m, dj3m, aej3m, bdej3m, bfj3m, adfj3m, af2j3m, am2, dm2, abem2, fm2, abdfm2, ajm2, bdjm2, abejm2, dejm2, fjm2, adfjm2, aj2m2, bdj2m2, abej2m2, dej2m2, aj3m2, bdj3m2, abej3m2, dej3m2, bkm2, am3, dm3, bdem3, abjm3, djm3, abj2m3, dj2m3, abj3m3, dj3m3, n, acn, abdn, cdn, ben, aden, bcden, afn, cfn, dfn, abcdfn, abefn, bdefn, f2n, adf2n, abdef2n, abgn, dgn, fgn, adfgn, af2gn, hn, abdhn, abfhn, dfhn, bh2n, eh2n, h3n, abdh3n, aein, bdein, bfin, adfin, af2in, bdf2in, abhin, ah2in, bdh2in, i2n, abdi2n, bei2n, adei2n, bdi3n, aei3n, ejn, abdejn, acfjn, bcdfjn, agjn, bdgjn, ehjn, eh2jn, abijn, dijn, fijn, abdfijn, i2jn, abdi2jn, abi3jn, di3jn, acj2n, bcdj2n, ej2n, adej2n, afj2n, dfj2n, bdefj2n, f2j2n, abdf2j2n, agj2n, dgj2n, fgj2n, abfhj2n, dfhj2n, bfij2n, adfij2n, af2ij2n, bdf2ij2n, bcdj3n, ej3n, abdej3n, abfj3n, acfj3n, abdf2j3n, agj3n, bdgj3n, bdfhj3n, abij3n, dij3n, fij3n, abdfij3n, df2ij3n, acj4n, cdj4n, ej4n, adej4n, afj4n, dfj4n, bdefj4n, f2j4n, adf2j4n, agj4n, dgj4n, fgj4n, adfgj4n, abfj5n, ahkn, i3kn, ai2jkn, bdi2jkn, aeln, bdeln, bfln, adfln, biln, ai2ln, bdi2ln, aejln, bdejln, fjln, abdfjln, aej2ln, bdej2ln, bfj2ln, adfj2ln, aej3ln, bdej3ln, fj3ln, abdfj3ln, befj3ln, adfj4ln, bl2n, el2n, ejl2n, ej2l2n, ael3n, bmn, admn, afmn, bdfmn, bf2mn, abimn, dimn, bi2mn, adi2mn, bjmn, adjmn, afjmn, bdfjmn, bj2mn, adj2mn, afj2mn, bdfj2mn, bf2j2mn, bj3mn, adj3mn, afj3mn, bdfj3mn, abkmn, abj2kmn, m2n, abdm2n, jm2n, abdjm2n, j2m2n, abdj2m2n, j3m2n, abdj3m2n, ajkm2n, bm3n, adm3n, bjm3n, adjm3n, bj2m3n, adj2m3n, bj3m3n, adj3m3n, bcn2, abdn2, acdn2, aben2, den2, abf2n2, df2n2, bgn2, adgn2, ahn2, bfhn2, abh2n2, ah3n2, adin2, ein2, abdein2, afin2, dfin2, f2in2, bhin2, h2in2, abei2n2, dei2n2, i3n2, adi3n2, abdei3n2, cjn2, abcdjn2, aejn2, dejn2, fjn2, adfjn2, abdefjn2, af2jn2, bdf2jn2, gjn2, adgjn2, afgjn2, fhjn2, bijn2, adijn2, afijn2, bdfijn2, bf2ijn2, ai2jn2, bdi2jn2, bi3jn2, adi3jn2, abj2n2, bcj2n2, acdj2n2, dej2n2, bgj2n2, bij2n2, adij2n2, cj3n2, abcdj3n2, aej3n2, dej3n2, fj3n2, adfj3n2, befj3n2, abdefj3n2, gj3n2, adgj3n2, afgj3n2, bij3n2, adij3n2, abj4n2, bcj4n2, acdj4n2, dej4n2, bgj4n2, fj5n2, adfj5n2, abijkn2, dijkn2, abi3jkn2, di3jkn2, adj2kn2, adj4kn2, beln2, abfln2, aefln2, abiln2, i2ln2, bejln2, abfj2ln2, amn2, dmn2, bdemn2, fmn2, adfmn2, af2mn2, imn2, abdimn2, ai2mn2, di2mn2, aejmn2, bdejmn2, bfjmn2, adfjmn2, af2jmn2, abj2mn2, dj2mn2, aej2mn2, aej3mn2, abm2n2, dm2n2, ajm2n2, djm2n2, abejm2n2, abej2m2n2, aj3m2n2, bdj3m2n2, abej3m2n2, bkm2n2, am3n2, dm3n2, n3, acn3, abdn3, cdn3, ben3, aden3, afn3, cfn3, dfn3, abefn3, bdefn3, f2n3, adf2n3, abdef2n3, abgn3, dgn3, hn3, abfhn3, bfin3, adfin3, af2in3, i2n3, abdi2n3, bdi3n3, ejn3, abdejn3, acfjn3, agjn3, bdgjn3, abijn3, dijn3, fijn3, abdfijn3, i2jn3, abdi2jn3, abi3jn3, di3jn3, acj2n3, adj2n3, bcdj2n3, ej2n3, abdej2n3, afj2n3, dfj2n3, bdefj2n3, agj2n3, dgj2n3, acj3n3, bcdj3n3, ej3n3, abdej3n3, abfj3n3, dfj3n3, agj3n3, bdgj3n3, abij3n3, dij3n3, acj4n3, adj4n3, cdj4n3, ej4n3, abdej4n3, afj4n3, dfj4n3, agj4n3, dgj4n3, aeln3, bfln3, aejln3, fjln3, bfj2ln3, bmn3, admn3, afmn3, bdfmn3, bf2mn3, bjmn3, adjmn3, afjmn3, bdfjmn3, bj2mn3, adj2mn3, bj3mn3, adj3mn3, abkmn3, abj2kmn3, m2n3, adm2n3, abdem2n3, ejm2n3, ej2m2n3, bm3n3, adm3n3, bcn4, abdn4, acdn4, aben4, den4, abf2n4, df2n4, bgn4, adgn4, cjn4, abcdjn4, aejn4, dejn4, fjn4, adfjn4, af2jn4, bdf2jn4, gjn4, adgjn4, abj2n4, bcj2n4, acdj2n4, dej2n4, bgj2n4, aej3n4, dej3n4, fj3n4, adfj3n4, gj3n4, adgj3n4, abej4n4, dej4n4, bgj4n4, adgj4n4, adj2kn4, amn4, dmn4, abj2mn4, dj2mn4, abm2n4, dm2n4, abjm2n4, djm2n4, abj2m2n4, dj2m2n4, am3n4, dm3n4, n5, abdn5, ben5, aden5, afn5, dfn5, ejn5, abdejn5, adj2n5, ej2n5, abdej2n5, afj2n5, dfj2n5, ej3n5, abdej3n5, abfj3n5, ej4n5, adej4n5, bmn5, admn5, bjmn5, adjmn5}

Phi = 1 a b c2 c 1 d ac2 e f ad c2 g h i j k l m n

Monoid Structure

Idempotent  |G|  |Arch|
122
b288
c2 *83338
h21624
ahi1616
i21624
h3j1640
i2j23256
j41640
il1616
l21624
j2l21648
dim1616
adi2jm1616
m21624
j2m23272
h2n2840
ahin2824
i2n264192
h3jn2856
iln2824
aj3ln2872
l2n2840
dimn21632
n41640
j4n432200
m2n416104
j2m2n432216