Lewis Mammel, <a href="/A145384/b145384.txt">Table of n, a(n) for n = 1..122</a>

nonn,new

nonn

0 = number of terms of A050791 preceding the 1st first term of A141326

1 = number of terms of A050791 between the 1st first and 2nd terms of A141326

nonn,new

nonn

A141326 is a simply generated subsequence of A050791, and by observation it forms a natural measure of the parent sequence. The first several hundred terms of the parent sequence not belonging to A141326 are bracketed into groups with a small integral number of terms ( including 0 ) by the successive terms of the subsequence, A141326.

a(107),a(108) are the first occurrence of 2 consecutive 0's, and a(119),a(120),a(121) are the first occurrence of 3 consecutive 0's. This leads to the following conjecture:

Lewis Mammel, <a href="http://www.research.att.com/~njas/sequences/b145384.txt">Table of n, a(n) for n = 1..122</a>

nonn,new

nonn

The number of terms of A050791 bracketed by successive terms of A141326

0, 1, 2, 3, 2, 3, 2, 2, 6, 6, 0, 3, 1, 3, 2, 3, 2, 4, 4, 3, 0, 3, 5, 0, 2, 2, 3, 2, 1, 2, 3, 1, 2, 3, 5, 1, 1, 4, 2, 0, 1, 3, 1, 3, 3, 2, 2, 2, 4, 2, 1, 2, 4, 2, 0, 1, 2, 3, 1, 1, 1, 3, 0, 3, 1, 0, 3, 1, 1, 4, 2, 2, 1, 3, 3, 1, 2, 0, 3, 2, 5, 1, 1, 3, 6, 2, 4, 1, 0, 5, 2, 2, 2, 2, 3, 2, 3, 3, 0, 1

1,3

A141326 is a simply generated subsequence of A050791, and by observation it forms a natural measure of the parent sequence. The first several hundred terms of the parent sequence not belonging to A141326 are bracketed into groups with a small integral number of terms ( including 0 ) by the successive terms of the subsequence, A141326.

a(107),a(108) are the first occurrence of 2 consecutive 0's, and a(119),a(120),a(121) are the first occurrence of 3 consecutive 0's. This leads to the following conjecture:

<a(n)> -> 0 as n ->inf

where <a(n)> = ( sum m=1,n of a(m) )/n

Lewis Mammel, <a href="http://www.research.att.com/~njas/sequences/b145384.txt">Table of n, a(n) for n = 1..122</a>

a(1) = A145383(1) - 1

a(n) = A145383(n) - A145383(n-1) - 1 ; n>1

0 = number of terms of A050791 preceding the 1st term of A141326

1 = number of terms of A050791 between the 1st and 2nd terms of A141326

2 = number of terms of A050791 between the 2nd and 3rd terms of A141326

Cf. A145383, A141326, A050791

nonn

Lewis Mammel (l_mammel(AT)att.net), Oct 10 2008

approved