A178164 Decimal expansion of the largest arbitrarily-long Type-2 Trott-like constant (see A178160 for definition).

9, 9, 1, 9, 9, 1, 9, 9, 9, 7, 9, 8, 9, 9, 9, 3, 7, 9, 9, 1, 1, 9, 9, 3, 2, 9, 9, 2, 9, 9, 9, 1, 9, 9, 9, 1, 5, 9, 9, 1, 1, 9, 9, 9, 9, 9, 9, 1, 4, 9, 9, 1, 6, 9, 9, 1, 7, 9, 9, 1, 1, 9, 9, 1, 3, 9, 9, 1, 5, 9, 9, 1, 9, 9, 9, 1, 1, 9, 9, 6, 9, 9, 9, 1, 9, 9, 9, 4, 4, 9, 9, 1, 8, 9, 9, 1, 1, 9, 9, 1, 2, 9, 9, 2, 9

Offset

0,1

Comments

For n=1,2,..., the largest n-digit numbers in A178160 are 9, 99, 991, 9919, etc., so a(1)=9, a(2)=9, a(3)=1, a(4)=9, etc.

The number of digits of agreement increases as more digits are used, but the ratio (digits of agreement divided by digits used) is between 0.31 and 0.32 when the number of digits used is between a few hundred and a few thousand; this rate of convergence is not nearly as good as that of the second Trott constant (A091694).

Links

Jon E. Schoenfield, Table of n, a(n) for n = 0..3999

Example

0+9/(9+1/(9+9/(1+9/(9+9/(7+9/(8+9/(9+9/(3+7/(9+9/...))))))))) = 0.9919919997989993799...

Crossrefs

Cf. A091694, A113307, A178160.

Sequence in context: A144667 A118428 A166925 * A216035 A171487 A371996

Adjacent sequences: A178161 A178162 A178163 * A178165 A178166 A178167

Keyword

nonn,cons

Author

Jon E. Schoenfield, May 21 2010

Status

approved