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A034180 Numbers m with property that rotating digits of m right gives k*m + 1 for some k >= 1.

%I A034180 #21 Apr 23 2022 16:07:44
%S A034180 103,1052,1139,2758,26315,206896,1012658,15789473,137931034,183673469,
%T A034180 3157894736,421052631578,1020408163265,2105263157894,13559322033898,
%U A034180 36842105263157,241379310344827,1525423728813559,11392405063291139
%N A034180 Numbers m with property that rotating digits of m right gives k*m + 1 for some k >= 1.
%H A034180 Chai Wah Wu, <a href="/A034180/b034180.txt">Table of n, a(n) for n = 1..958</a>
%e A034180 Rotating 103 gives 310 and 310 = 3 * 103 + 1. - _Sean A. Irvine_, Aug 04 2020
%o A034180 (Python)
%o A034180 from itertools import count, islice
%o A034180 def A034180_gen(): # generator of terms
%o A034180     for l in count(1):
%o A034180         clist = []
%o A034180         for k in range(1,10):
%o A034180             a, b = 10**l-k, 10**(l-1)-k
%o A034180             for m in range(1,10):
%o A034180                 q, r = divmod(m*a-1,10*k-1)
%o A034180                 if r == 0 and b <= q - k <= a:
%o A034180                     clist.append(10*q+m)
%o A034180         yield from sorted(clist)
%o A034180 A034180_list = list(islice(A034180_gen(),20)) # _Chai Wah Wu_, Apr 23 2022
%K A034180 nonn,base
%O A034180 1,1
%A A034180 _Erich Friedman_
%E A034180 Terms sorted and title clarified by _Sean A. Irvine_, Aug 04 2020
%E A034180 a(19) corrected by _Chai Wah Wu_, Apr 23 2022