Details Page for 0.4107

Complete Solution is Known:

Period:   24
Preperiod:   66
Quotient Size:   506
P-Portion Size:   58
Tame?   No

MSV File: q-0.4107.msv

Growth Pattern:

Heap   Q-Size   P-Size
221
462
7102
9184
10204
13366
15527
17609
187210
197611
229613
2412417
3012618
3328036
3532240
3632841
3741046
3943648
4144848
4345249
4445650
4646452
4746652
5046853
5147454
5348055
5648857
6150658

(Click on a heap to see details)

Details for Q43(0.4107):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,A | a2=1, b5=b3, b3c2=b3, b2c3=b2c, c4=c2, bd=ab3, c3d=cd, d2=b4, be=ab, ce=ac, de=ad, e3=ae2, bf=b4, c3f=cf, df=ab3, ef=af, f2=b4, b3g=ab4c, bcg=ab2c2, c2g=abc3, dg=ab2g, eg=ag, cfg=ab4, g2=b2, b2h=ab3, bc3h=bch, dh=b3, eh=ah, fh=ab4, bgh=ab2g, cgh=abc2h, h2=b4, b3i=b3c, bc2i=bi, c3i=ci, c2di=di, ei=ai, fi=b3c, bgi=ab2ci, cgi=abi, c2hi=hi, ghi=abchi, i2=b2ci, bj=ab3, c3j=cj, c2dj=dj, ej=aj, fj=ab3, gj=ab2g, hj=b3, ij=bhi, j2=b4, bk=bc, c2dk=dk, ek=ak, cfk=c2f, cgk=abc, fgk=ab4, hk=ch, c2ik=ik, dik=bchi, gik=abi, c2jk=jk, djk=b4c, k2=ck, bl=ab2c, c3l=cl, dl=b3c, el=al, fl=ab4c, cgl=b2c, hl=abch, c2il=il, gil=b2i, jl=b3c, kl=cl, l2=b2ci, b2m=ab3c, bc2m=bm, c3m=cm, dm=b3c, em=am, fm=ab4c, gm=abcm, bhm=b3c, c2hm=hm, bim=ab2ci, c2im=im, jm=b3c, km=cm, lm=abcm, m2=b4, bn=b2, dn=ab3, en=an, fn=b4, cgn=ab2c2, hn=bh, in=acil, jn=ab3, kn=cn, ln=ab2i, mn=bm, n2=b4, b2o=b3, bc2o=bo, do=ab3, eo=ao, fo=b4, bgo=ab3c, cgo=abo, ho=abo, bio=chim, c2io=io, gio=ahim, jo=ab3, ko=co, lo=achim, mo=abco, no=b4, o2=b4, bp=ab3, cp=ab2c, dp=b4, ep=ap, fp=ab3, gp=ab2g, hp=b3, ip=ab2i, jp=b4, kp=ab2c, lp=b3c, mp=b3c, np=ab3, op=ab3, p2=b4, b2q=b2i, bcq=aim, c3q=cq, c2dq=dq, eq=aq, fq=b3c, gq=im, bhq=achim, c2hq=hq, biq=b3, c2iq=iq, diq=adj, hiq=ab3, jq=bhi, c2kq=kq, dkq=bchi, ikq=b2i, c2lq=lq, ilq=ab3c, bmq=ab4, c2mq=mq, hmq=him, imq=ab3c, cnq=alq, oq=io, pq=ab2i, bq2=b3, c2q2=q2, dq2=adj, hq2=ab3, iq2=b4c, kq2=b2i, lq2=ab3c, mq2=ab3c, nq2=b3, q3=b4c, b2r=b4c, cr=b2, dr=ab4c, er=ar, fr=ab2g, hr=abr, ir=b2ci, jr=ab4c, kr=b2, lr=ab3, mr=ab3, nr=b3c, or=ab2g, pr=ab4c, qr=b2ci, r2=b4, bs=acjk, ds=ab3, es=as, fs=b4, gs=jk, c2hs=hs, c2is=is, his=bhi, js=ab3, ks=cs, ls=bhi, ms=chs, ns=b4, os=b4, ps=ab3, c2qs=qs, hqs=achim, iqs=b3, q2s=b3, rs=b3c, s2=b4, bt=ab2i, c3t=ct, dt=b3c, et=at, ft=ab4c, cgt=b2i, ht=hm, c2it=it, git=b4c, jt=b3c, kt=ct, lt=b4, mt=b4, nt=ab4c, ot=ab4c, pt=b3c, qt=it, rt=ab3, st=ab4c, t2=b4, b2u=abo, c3u=cu, du=bo, eu=au, cgu=abc2u, bc2hu=bhu, bhiu=chim, ju=bo, ku=cu, c2lu=lu, glu=abo, bmu=bchu, c2mu=mu, hmu=ab4c, imu=chiu, c2nu=nu, gnu=bco, ou=fu, pu=bo, bqu=ahiu, hqu=b3c, iqu=ahim, mqu=b3, nqu=aclqu, q2u=ahim, su=nu, tu=clqu, u2=b4, bv=b2ci, c3v=cv, dv=ab3, ev=av, fv=b2ci, cgv=ab2ci, c2hv=hv, ghv=b3c, civ=ait, giv=bgr, hiv=achim, jv=ab3, kv=cv, lv=ab4c, mv=ab4c, nv=b4, ov=b2ci, pv=ab3, qv=acit, rv=b3c, sv=b4, tv=ab4c, huv=him, iuv=bru, v2=b4, bw=ab4c, c3w=cw, dw=b3c, ew=aw, fw=ab4c, gw=bgru, hw=hm, iw=it, jw=b3c, kw=cw, lw=b4, mw=b4, nw=ab4c, ow=ab4c, pw=b3c, qw=it, rw=ab3, sw=ab4c, tw=b4, uw=b3c, vw=ab4c, w2=b4, b2x=bru, bcx=abgru, c2x=cfu, dx=abru, ex=ax, cfx=ab4, cgx=afx, fgx=b3, bhx=abru, chx=bgru, bix=ab4, cix=ab3c, gix=fgu, hix=b4, jx=abru, fkx=abgru, ikx=ab3c, lx=bgru, mx=bgru, cnx=abgru, gnx=gru, ox=agkx, px=abru, qx=ghx, brx=abgru, sx=agrx, tx=b4, ux=b3c, vx=aguv, wx=b4, x2=b4, by=br, c2y=b2i, dy=ab4c, ey=ay, fy=br, cgy=b2g, hy=abr, ciy=b4c, giy=b2g, jy=ab4c, ky=cy, ly=ab3, my=ab3, ny=b3c, oy=br, py=ab4c, qy=abgr, ry=b4, sy=b3c, ty=ab3, cuy=ahim, iuy=abgru, vy=b3c, wy=ab3, cxy=bru, ixy=bru, y2=b4, bz=abgx, dz=bgru, ez=az, fz=ab3, cgz=b3, hz=aghx, ciz=ahim, giz=b3, jz=bgru, kz=cz, lz=b3c, mz=b3c, nz=agru, oz=ab3, pz=bgru, qz=achim, rz=agrx, sz=ab3, tz=b3c, uz=him, vz=ab3, wz=b3c, xz=b3c, yz=agxy, z2=b4, bA=ab4c, cA=ab3, dA=b3c, eA=aA, fA=ab4c, hA=b4c, iA=ab3, jA=b3c, kA=ab3, lA=b4, mA=b4, nA=ab4c, oA=ab4c, pA=b3c, qA=ab3, rA=ab3, sA=ab4c, tA=b4, uA=abru, vA=ab4c, wA=b4, xA=bgru, yA=ab3, zA=b3c, A2=b4>

P = {a, b2, b4, c2, b2c2, acd, e2, ah, abch, b2ci, achi, cj, ck, c3k, adk, al, abcm, hm, ao, ac2o, acio, cq, adq, achq, kq, q2, abgr, as, ac2s, acis, acqs, at, abu, abc2u, hu, c2hu, abciu, giu, chiu, clu, cmu, abru, achv, acuv, aw, ackx, cy, iy, aA}

Phi = 1 1 a a b b ab c c d e f g h b i ab2 j k l m n o p q r abo anq b3 s t abm cq2 u cjk v w x b3 y agt z b2i A

Monoid Structure

Idempotent  |G|  |Arch|
122
b4 *8432
c246
e224
c3k48