OFFSET
1,1
COMMENTS
The number of members in the n-th row appears to be equal to 2 + ( (n) * ((1 + sqrt(5))/2) ), or the n-th member of the lower Wythoff sequence (A000201) plus two. For the four rows show above, these values are 3, 5, 6, 8.
The first member of each row n is the number of primes in the set {2^n...2^(n + 1) - 1} (sequence A036378). The last member of each row follows sequence A092097, which is also equivalent to taking the difference of successive members of A052130 (the number of products of half-odd primes less than 2^n).
EXAMPLE
Let x = 1. In set {2^2..2^(3) - 1}, or {4, 5, 6, 7}, S{n - 1} = S(2 - 1} = S{1} = subset of all numbers with one factor (the primes). The size of this subset is 2, or {5, 7}. For the set {2^3...2^(4) - 1}, the size of subset S{3 - 1} is 4. For {2^4..2^(5) - 1}, the size of subset S{4 - 1} is 5. For all subsequent sets, the size of subset S{n - 1} will be 5.
The triangle begins:
2,4,5
2,4,6,7,8
5,12,17,20,21,22
7,20,30,37,41,44,46,47
...
CROSSREFS
KEYWORD
easy,nonn,tabf
AUTHOR
Andrew S. Plewe, Jun 29 2004
STATUS
approved