A046734 - OEIS

%I #10 Dec 18 2015 10:05:17

%S 1,1,13,4,31,13,48,8,39,31,110,52,168,48,403,16,96,39,360,124,624,110,

%T 553,104,155,168,117,48,140,403,331,32,1430,96,1488,156,469,360,2184,

%U 248,560,624,308,220,1209,553,46,208,336,155,1248,168,52,117

%N Period of A000213 mod n.

%H Charles R Greathouse IV, <a href="/A046734/b046734.txt">Table of n, a(n) for n = 1..1000</a>

%H Nick Hobson, <a href="/A046734/a046734.py.txt">Python program for this sequence</a>

%o (PARI) isper(v,startAt=1)=for(k=startAt,#v-3, for(i=1,3,if(v[i]!=v[k+i],next(2)));return(k)); 0

%o ap(p)=my(v=vector(99),t); v[1]=v[2]=v[3]=1; for(i=4,#v,v[i]=sum(j=i-3,i-1,v[j])%p); while((t=isper(v,if(#v>99,#v/2-2,1)))==0, v=concat(v, vector(#v)); for(i=#v/2+1,#v, v[i]=sum(j=i-3,i-1,v[j])%p));t

%o ape(p,e)=if(p==2, return(if(e>1,p^e,1))); if(e==1, return(ap(p))); my(pe=p^e, P=ap(p)*p^(e-1), v=vector(P+3)); v[1]=v[2]=v[3]=1; for(i=4,#v,v[i]=sum(j=i-3,i-1,v[j])%pe); isper(v)

%o a(n)=my(f=factor(n)); lcm(vector(#f~, i, ape(f[i,1],f[i,2]))) \\ _Charles R Greathouse IV_, Dec 10 2015

%K nonn

%O 1,3

%A _David W. Wilson_