Details Page for 0.7135

Complete Solution is Known:

Period:  
Preperiod:  
Quotient Size:   860
P-Portion Size:   145
Tame?   No

MSV File: q-0.7135.msv

Growth Pattern:

Heap   Q-Size   P-Size
121
262
5144
7164
10244
11366
14407
16528
17568
209212
229612
2313619
2414820
2518826
2622433
2724036
2828043
2933651
3035255
3138859
3245669
3346872
3450476
3556886
3658089
3762096
38696112
39708115
40764125
41848142
42860145

(Click on a heap to see details)

Details for Q42(0.7135):

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,B,C,D,E | a2=1, b3=b, b2c=c, c11=ac10, bd=ab, cd=ac, d2=b2, b2e=e, c2e=abc3, de=ae, ce2=c3, e9=bc10, b2f=f, cf=abce, df=af, e8f=ac10, ef2=abe2f, f9=ac10, b2g=g, c2g=ac4, dg=ag, ceg=bc4, e7g=abc10, e6fg=c10, f3g=e2fg, cg2=c5, e2g2=ae4g, fg2=ae2fg, g3=e4g, b2h=h, ch=abcg, dh=ah, e2h=ae3f, f2h=bf4, fgh=be2fg, g2h=e3fg, h2=f4, b2i=i, ci=cg, di=ai, e3i=e3g, efi=efg, f2i=abefg, egi=eg2, fgi=egh, ehi=ae2fg, fhi=abegh, ei2=ae3g, fi2=egh, gi2=g2i, hi2=e3fg, i3=e4g, b2j=j, c2j=abc5, dj=aj, cej=c5, e2j=ae3g, efj=egh, f2j=be2fg, cgj=bc6, egj=g2i, fgj=e3fg, g2j=ae5g, hj=e2fg, eij=e4g, fij=ghi, i2j=ae5g, j2=ae4g, b2k=k, ck=abcj, dk=ak, e2k=e4f, f2k=f5, egk=ghi, fgk=abe3fg, g2k=ae4fg, hk=bf5, eik=e3fg, fik=abghi, i2k=ae4fg, jk=ae3fg, k2=f6, b2l=l, c2l=ac6, dl=al, el=ij, fl=gk, cgl=c7, g2l=e6g, hl=ae3fg, i2l=e6g, jl=e5g, kl=e4fg, l2=ae6g, b2m=m, c3m=bc7, dm=am, cem=abc2m, e2m=ae5f, f2m=bf6, cgm=abc7, egm=gik, fgm=be4fg, g2m=e5fg, hm=f6, eim=ae4fg, fim=abgik, i2m=e5fg, jm=e4fg, km=bf7, lm=ae5fg, m2=f8, b2n=n, cn=abcm, dn=an, e2n=e4g, efn=ghi, f2n=abe3fg, gn=gl, hn=ae3fg, in=il, jn=e5g, kn=e4fg, ln=ae6g, mn=ae5fg, n2=ae6g, b2o=o, c3o=abc8, do=ao, ceo=abc2o, e2o=ae5g, efo=gik, f2o=be4fg, cgo=bc8, ego=gil, fgo=e5fg, g2o=bc10, ho=e4fg, eio=e6g, fio=gim, i2o=bc10, jo=ae6g, ko=ae5fg, lo=abc10, mo=c10, no=abc10, o2=c10, b2p=p, c4p=c9, dp=ap, cep=abc2p, e3p=e7f, efp=abe2p, f3p=f8, cgp=ac3p, egp=e5fg, fgp=abe5fg, g2p=ac10, hp=bf2p, ip=gp, jp=ae5fg, kp=f8, lp=c10, mp=abc10, np=c10, op=abc10, p2=c10, b2q=q, cq=abcp, dq=aq, e3q=ae6g, efq=agp, f3q=ae5fg, gq=ae2q, hq=bf2q, iq=ae2q, jq=ae6g, kq=ae5fg, lq=abc10, mq=c10, nq=abc10, oq=c10, pq=abc10, q2=c10, b2r=r, c4r=ac10, dr=ar, cer=abc2r, e3r=abc10, e2fr=bgio, f3r=c10, gr=ae2r, ehr=abgio, fhr=bc10, ir=ae2r, jr=abc10, kr=c10, lr=c10, mr=abc10, nr=c10, or=abc10, pr=c10, qr=abc10, r2=c10, b2s=s, c4s=gio, ds=as, ces=abc2s, e4s=bc10, efs=abe2s, f3s=abe3s, cgs=ac3s, e2gs=abc10, fgs=abegs, g2s=bc10, hs=bf2s, is=gs, js=aegs, ks=abe3s, ls=abc10, ms=c10, ns=abc10, os=c10, ps=abc10, qs=c10, rs=abc10, s2=c10, b2t=t, ct=abcs, dt=at, e3t=begs, eft=ags, f3t=e3s, gt=ae2t, ht=bf2t, it=ae2t, jt=begs, kt=e3s, lt=c10, mt=abc10, nt=c10, ot=abc10, pt=c10, qt=abc10, rt=c10, st=abc10, t2=c10, b2u=u, c4u=gio, du=au, ceu=abc2u, e4u=bc10, e2fu=c3u, f4u=bc10, gu=ae2u, ehu=ac3u, fhu=bf3u, iu=ae2u, ju=e3u, eku=abgio, fku=bc10, lu=abc10, mu=c10, nu=abc10, ou=c10, pu=abc10, qu=c10, ru=abc10, su=c10, tu=abc10, u2=c10, b2v=v, c3v=aefu, dv=av, cev=abc2v, e4v=ae3s, efv=abe2v, f2v=e2v, cgv=efu, e2gv=aegs, fgv=abegv, g2v=egs, hv=be2v, iv=gv, jv=aegv, kv=abe3v, lv=aegs, mv=abe3s, nv=aegs, ov=abc10, pv=c10, qv=abc10, rv=c10, sv=abc10, tv=c10, uv=abc10, v2=c10, b2w=w, cw=abcv, dw=aw, e2w=bgv, efw=agv, f4w=be3s, gw=abgv, hw=bf2w, iw=abgv, jw=begv, kw=f3w, lw=begs, mw=e3s, nw=begs, ow=c10, pw=abc10, qw=c10, rw=abc10, sw=c10, tw=abc10, uw=c10, vw=abc10, w2=c10, b2x=x, c3x=aefu, dx=ax, cex=abc2x, e3x=ae2u, efx=abc2x, f3x=bf2u, gx=ae2x, hx=bf2x, ix=ae2x, jx=ae2u, kx=hu, lx=e3u, mx=ku, nx=e3u, ox=abc10, px=c10, qx=abc10, rx=c10, sx=abc10, tx=c10, ux=abc10, vx=c10, wx=abc10, x2=c10, b2y=y, c3y=bc2x, dy=ay, cey=abc2y, e3y=ae2v, fy=abey, cgy=abc2x, egy=agv, g2y=egv, hy=be2y, iy=gy, jy=gv, ky=be2v, ly=aegv, my=abe3v, ny=aegv, oy=aegs, py=abe3s, qy=aegs, ry=abc10, sy=c10, ty=abc10, uy=c10, vy=abc10, wy=c10, xy=abc10, y2=c10, b2z=z, cz=abcy, dz=az, e2z=bgy, efz=agy, f3z=bf2w, gz=abgy, hz=bf2z, iz=abgy, jz=abgv, kz=bf2w, lz=begv, mz=f3w, nz=begv, oz=begs, pz=e3s, qz=begs, rz=c10, sz=abc10, tz=c10, uz=abc10, vz=c10, wz=abc10, xz=c10, yz=abc10, z2=c10, b2A=A, c2A=c2y, dA=aA, ceA=abc2y, e2A=aex, efA=abc2y, f2A=bfx, gA=ex, hA=fx, iA=ex, jA=ae2x, kA=bf2x, lA=ae2u, mA=hu, nA=ae2u, oA=e3u, pA=ku, qA=e3u, rA=abc10, sA=c10, tA=abc10, uA=c10, vA=abc10, wA=c10, xA=abc10, yA=c10, zA=abc10, A2=c10, b2B=B, c2B=bcA, dB=aB, ceB=acA, e2B=aeA, efB=acA, f2B=bfA, gB=eA, hB=fA, iB=eA, jB=ex, kB=fx, lB=ae2x, mB=bf2x, nB=ae2x, oB=ae2u, pB=hu, qB=ae2u, rB=e3u, sB=ku, tB=e3u, uB=abc10, vB=c10, wB=abc10, xB=c10, yB=abc10, zB=c10, AB=abc10, B2=c10, b2C=C, c2C=bcB, dC=aC, ceC=acB, e2C=aeB, efC=acB, f2C=bfB, gC=eB, hC=fB, iC=eB, jC=eA, kC=fA, lC=ex, mC=fx, nC=ex, oC=ae2x, pC=bf2x, qC=ae2x, rC=ae2u, sC=hu, tC=ae2u, uC=e3u, vC=ku, wC=e3u, xC=abc10, yC=c10, zC=abc10, AC=c10, BC=abc10, C2=c10, b2D=D, c2D=bcC, dD=aD, ceD=acC, e4D=aey, fD=abeD, cgD=acB, e2gD=abez, g2D=bez, hD=be2D, iD=gD, jD=aegD, kD=abe3D, lD=abez, mD=abey, nD=abez, oD=gy, pD=be2y, qD=gy, rD=gv, sD=be2v, tD=gv, uD=aegv, vD=abe3v, wD=aegv, xD=aegs, yD=abe3s, zD=aegs, AD=abc10, BD=c10, CD=abc10, D2=c10, b2E=E, cE=abcD, dE=aE, e2E=bgD, efE=agD, f4E=bfz, gE=abgD, hE=bf2E, iE=abgD, jE=begD, kE=f3E, lE=ez, mE=fz, nE=ez, oE=abgy, pE=bf2z, qE=abgy, rE=abgv, sE=bf2w, tE=abgv, uE=begv, vE=f3w, wE=begv, xE=begs, yE=e3s, zE=begs, AE=c10, BE=abc10, CE=c10, DE=abc10, E2=c10>

P = {a, b2, abc, c2, ac3, c4, ac5, c6, ac7, c8, ac9, c10, e2, be3, e4, be5, e6, be7, e8, aef, abe3f, ae4f, abe5f, ae6f, abe7f, f2, af3, f4, af5, f6, af7, f8, aeg, abe3g, ae4g, abe5g, ae6g, fg, e2fg, be3fg, e4fg, be5fg, af2g, g2, bh, eh, abfh, abgh, abei, ae2i, bfi, bgi, abhi, i2, aj, bl, am, cm, bn, co, bp, abcp, bc2p, ae2p, af2p, abeq, bf2q, br, abcr, bc2r, er, aefr, abhr, cs, ac2s, c3s, abes, e3s, fs, gs, et, be2t, abft, au, cu, ac2u, c3u, abeu, ae2u, fu, befu, af2u, abku, abcv, bc2v, ev, be2v, abfv, abgv, aegv, aw, abew, fw, af2w, bx, abcx, bc2x, ex, be2x, abfx, bf2x, ay, cy, ac2y, abey, ae2y, gy, bz, ez, abfz, bf2z, aA, cA, abeA, fA, bB, abcB, eB, abfB, aC, cC, abeC, fC, bD, abcD, eD, be2D, e3D, abgD, aegD, aE, abeE, fE, af2E, f3E}

Phi = 1 a b a b c b d b ab2 e f e g h i j k j l m n o p q r s t u v w x y z A e2D f2E B aeD bfE C D E

Monoid Structure

Idempotent  |G|  |Arch|
122
b246
c10 *4852