OFFSET
1,1
COMMENTS
a(n) is the smallest positive integer that is not contained in the n-th row of A215905.
a(n) >= n+1. In fact, for any m >= 1 there exists N >= 1 such that a(n) > mn for all n >= N. That is, this sequence grows super-linearly.
EXAMPLE
In the n = 4 case, there are unital *-subalgebras of dimensions 1 though 6, as follows:
a 0 0 0 ... a 0 0 0 ... a 0 0 0 ... a 0 0 0 ... a 0 0 0 ... a 0 0 0
0 a 0 0 ... 0 b 0 0 ... 0 b 0 0 ... 0 b 0 0 ... 0 a 0 0 ... 0 b 0 0
0 0 a 0 ... 0 0 b 0 ... 0 0 c 0 ... 0 0 c 0 ... 0 0 b c ... 0 0 c d
0 0 0 a ... 0 0 0 b ... 0 0 0 c ... 0 0 0 d ... 0 0 d e ... 0 0 e f
However, there is no unital *-subalgebra of the 4-by-4 matrices of dimension 7, so a(4) = 7.
CROSSREFS
KEYWORD
nonn
AUTHOR
Nathaniel Johnston, Aug 26 2012
STATUS
approved