A111936 Denominator of n-th term of the harmonic series after removal of all terms 1/m from Sum_{m=1..n} 1/m for which m contains a 9 in its decimal representation.

1, 2, 6, 12, 60, 20, 140, 280, 280, 3080, 9240, 120120, 120120, 40040, 80080, 1361360, 12252240, 2450448, 2450448, 2450448, 56360304, 56360304, 1409007600, 1409007600, 4227022800, 4227022800, 4227022800, 131037706800, 262075413600

Offset

1,2

Comments

Numerator = A111935;

lim_{n->infinity} A111935(n)/a(n) = C < 80.

References

G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part One, Chap. 3, sect. 4, Problem 124.

Links

Table of n, a(n) for n=1..29.

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) = 280.

Mathematica

Denominator[Accumulate[DeleteCases[Table[1/n, {n, 40}], _?(MemberQ[ IntegerDigits[ Denominator[#]], 9]&)]]] (* Harvey P. Dale, Mar 05 2013 *)

Prog

(Magma) a:=[k:k in [1..100]| not 9 in Intseq(k)]; [Denominator( &+[1/a[m]: m in [1..n]]): n in [1..30] ]; // Marius A. Burtea, Dec 29 2019

Crossrefs

Cf. A002805, A007095, A082838, A111935 (numerators).

Sequence in context: A083001 A285079 A119862 * A232090 A203811 A002805

Adjacent sequences: A111933 A111934 A111935 * A111937 A111938 A111939

Keyword

nonn,base,frac

Author

Reinhard Zumkeller, Aug 22 2005

Extensions

Definition edited by N. J. A. Sloane, Dec 30 2019

Status

approved