%I A111935
%S A111935 1,3,11,25,137,49,363,761,789,8959,27647,368651,377231,128413,261831,
%T A111935 4531207,41461543,8414831,8531519,8642903,201237217,203585563,
%U A111935 5145999379,5200191979,15757132337,15908097437,16048998197,501745966907
%N A111935 Numerator of n-th term of the harmonic series after having removed all 
               terms containing in decimal representation a 9.
%C A111935 Denominator = A111936;
%C A111935 a(n)/A111936(n) ---> C with C<80.
%C A111935 The sum of the harmonic series after having removed all terms containing 
               in decimal representation a 9 in decimal system converges and the 
               sum is < 80. Hence the sum of the harmonic series in which at least 
               one digit is missing ( from 0 to 9) converges and the sum is less 
               than 810.
%D A111935 G. Polya and G. Szego, Problems and Theorems in Analysis I (Springer 
               1924, reprinted 1972), Part One, Chap. 3, sect. 4, Problem 124.
%D A111935 Jason Earls and Amarnath Murthy, Some fascinating variations in harmonic 
               series, Octogon mathematical magazine, Vol. 12 No. 2, 2004.
%e A111935 n=9: 1/1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/10 = 789/280, therefore a(9) = 
               789.
%Y A111935 Cf. A001008, A007095.
%Y A111935 Sequence in context: A164303 A129082 A060746 this_sequence A001008 A096617 
               A025529
%Y A111935 Adjacent sequences: A111932 A111933 A111934 this_sequence A111936 A111937 
               A111938
%K A111935 nonn,base,frac
%O A111935 1,2
%A A111935 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 22 2005