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.

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

KEYWORD

nonn,cofr,more

AUTHOR

A.H.M. Smeets, Jan 02 2023

STATUS

approved