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A175555 Preperiodic part of the decimal expansion of 1/k as k runs through A065502.

%I A175555 #16 Oct 01 2012 15:32:05
%S A175555 5,25,2,1,125,1,8,0,0,625,0,5,0,41,4,0,3,0,3125,0,0,2,0,25,0,2,0,0,
%T A175555 208,2,1,0,0,17,0,1,0,15625,0,0,1,0,13,0,1,1,0,125,0,1,0,0,11,0,1,0,0,
%U A175555 1041,0,1
%N A175555 Preperiodic part of the decimal expansion of 1/k as k runs through A065502.
%C A175555 Multiples of 2 or 5 generate a quotient with a preperiodic sequence of digits, for example 1/24 = 0.041666666..., and 41 is the decimal form of the preperiodic part.
%C A175555 Usually a(n) = A114205(A065502(n)), but the convention in A114205 that leading zeros in the periodic part are attached to the preperiodic part seems not to be used here. - _R. J. Mathar_, Jul 20 2012
%e A175555 a(14)=4 is in the sequence because 1/25 = 0.040000... and 4 is the prefix.
%e A175555 208 is in the sequence because 1/48 = 2083333.... and 208 is the prefix.
%p A175555 A175555 := proc(n)
%p A175555         local k,s,al ;
%p A175555         k := A065502(n) ;
%p A175555         for s from 1 do
%p A175555                 for al from 0 to s-1 do
%p A175555                         if (10^s-10^al) mod k = 0 then
%p A175555                                 return floor(10^al/k) ;
%p A175555                         end if;
%p A175555                 end do:
%p A175555         end do:
%p A175555 end proc: # _R. J. Mathar_, Jul 22 2012
%Y A175555 Cf. A036275.
%K A175555 nonn,base
%O A175555 1,1
%A A175555 _Michel Lagneau_, Jun 29 2010