%I A034089
%S A034089 102564,128205,142857,153846,179487,205128,230769,102564102564,
%T A034089 128205128205,142857142857,153846153846,179487179487,205128205128,
%U A034089 230769230769,1012658227848,1139240506329,102564102564102564
%N A034089 Numbers which are proper divisors of the number you get by rotating digits 
               right once.
%C A034089 Let p(q) denote the period of the fraction q; then sequence is generated 
               by p( i / (10k-1)), k=2,3,4,5,6,7,8,9; k <= i <= 9 and the concatenations 
               of those periods, e.g. p(7/39)=a(5) p(2/19)=a(17).
%C A034089 Example if k=5: p((5+2)/49)=142857 which is in the sequence as the concatenations 
               142857142857, 142857142857142857,142857142857142857142857 etc. - 
               Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 02 2002
%C A034089 The i in p( i / (10k-1)) is the last digit of the period, while k is 
               equal to the ratio (right-rotated of p)/p. Thus no concatenation 
               of any different such p's can be in the sequence. There are 8*9/2 
               = 36 terms which are not concatenation of previous terms, the last 
               one being a[124]=1525423728813559322033898305084745762711864406779661016949 
               with 58 digits. The term a[3]=p(7/49) is the only period of length 
               (6) different from the length (42) of the other terms corresponding 
               to the same value of k. - M. F. Hasler, Nov 18 2007
%H A034089 M. F. Hasler, <a href="b034089.txt">Table of n, a(n) for n = 1..124</
               a>
%o A034089 (PARI) period(p,q,S=[])=until(setsearch(S,p),S=setunion(S,[p]);p=10*p%q);
               S=[];until(p==S[1],S=concat(S,p);p=10*p%q);S*10\q /* print list of 
               periods, right-rotated and ratio */ rotquo(n,d)={d=divrem(n,10);d[1]+=d[2]*10^#Str(d[1]);
               [n,d[1],d[1]/n]} for(k=2,9,for(i=k,9,print1( i/(10*k-1),"\t",rotquo(sum(j=1,
               #p=period(i,k*10-1),p[j]*10^(#p-j))))) /* build the sequence up to 
               the greatest period */ A034089()={local(S=[],p); for(k=2,9,for(i=k,
               9,S=concat(S,sum(j=1,#p=period(i,k*10-1),p[j]*10^(#p-j))))); S=vecsort(S); 
               for(i=1,#S, for(c=2,58\p=#Str(S[i]), S=concat(S,S[i]*(10^(c*p)-1)/
               (10^p-1)) )); vecsort(S)} \\ - M. F. Hasler, Nov 18 2007
%Y A034089 Sequence in context: A106814 A074669 A010329 this_sequence A146569 A081463 
               A014884
%Y A034089 Adjacent sequences: A034086 A034087 A034088 this_sequence A034090 A034091 
               A034092
%K A034089 easy,nice,nonn,base
%O A034089 1,1
%A A034089 Erich Friedman (erich.friedman(AT)stetson.edu)
%E A034089 Edited, corrected and extended by M. F. Hasler (Maximilian.Hasler(AT)gmail.com), 
               Nov 18 2007