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Search: id:A111935
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| A111935 |
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Numerator of n-th term of the harmonic series after having removed all terms containing in decimal representation a 9. |
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+0
2
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| 1, 3, 11, 25, 137, 49, 363, 761, 789, 8959, 27647, 368651, 377231, 128413, 261831, 4531207, 41461543, 8414831, 8531519, 8642903, 201237217, 203585563, 5145999379, 5200191979, 15757132337, 15908097437, 16048998197, 501745966907
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OFFSET
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1,2
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COMMENT
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Denominator = A111936;
a(n)/A111936(n) ---> C with C<80.
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.
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REFERENCES
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G. Polya and G. Szego, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part One, Chap. 3, sect. 4, Problem 124.
Jason Earls and Amarnath Murthy, Some fascinating variations in harmonic series, Octogon mathematical magazine, Vol. 12 No. 2, 2004.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A001008, A007095.
Sequence in context: A164303 A129082 A060746 this_sequence A001008 A096617 A025529
Adjacent sequences: A111932 A111933 A111934 this_sequence A111936 A111937 A111938
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KEYWORD
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nonn,base,frac
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 22 2005
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