A359457 Continued fraction for constant A359456.

0, 9, 11, 99, 1, 10, 9, 999999999999999999, 1, 8, 10, 1, 99, 11, 9

Offset

0,2

Comments

It seems that all terms smaller than 100 are identical to the continued fraction terms of Liouville's constant as in A058304.

Except for the first term, the only values that occur in this sequence are 1,8,9,10,11,and values 10^A359458(m-1)-1 for m > 1. The probability of occurrence P(a(n) = k) are given by:

P(a(n) = 1) = 1/4,

P(a(n) = 8) = 1/8,

P(a(n) = 9) = 1/8,

P(a(n) = 10) = 1/8,

P(a(n) = 11) = 1/8 and

P(a(n) = 10^A359458(m-1)-1 = 2^-(m+1) for m > 1.

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = 1 if and only if n in A317331,

a(n) = 8 if and only if n in A317332,

a(n) = 9 if and only if n in A317333,

a(n) = 10 if and only if n = 8*m - 6 + 3*(m mod 2) for m > 0,

a(n) = 11 if and only if n = 8*m - 3 - 3*(m mod 2) for m > 0,

a(n) = 10^A359458(m-1)-1 if and only if n in {2^m*(1+k*4) - 1 | k >= 0} union {2^m*(3+k*4) | k >= 0} for m > 1.

Crossrefs

Cf. A058304, A317331, A317332, A317333, A359456, A359458.

Sequence in context: A053886 A137020 A058304 * A365221 A027727 A019328

Adjacent sequences: A359454 A359455 A359456 * A359458 A359459 A359460

Keyword

nonn,cofr,more

Author

A.H.M. Smeets, Jan 02 2023

Status

approved