

A111935


Numerator of nth term of the harmonic series after having removed all terms containing in decimal representation a 9.


1



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

1,2


COMMENTS

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.


REFERENCES

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.


LINKS

Table of n, a(n) for n=1..28.


EXAMPLE

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.


CROSSREFS

Cf. A001008, A007095.
Sequence in context: A129082 A190476 A060746 * A175441 A001008 A231606
Adjacent sequences: A111932 A111933 A111934 * A111936 A111937 A111938


KEYWORD

nonn,base,frac


AUTHOR

Reinhard Zumkeller, Aug 22 2005


STATUS

approved



