I don't know if this is interesting to anyone, but... Eons ago, I came up with a notation for an expansion of n, inspired by continued fractions together with how close 3 1/7 is to pi: a + b\(1+c\(1+d\(1+...)...)) where "\" is read as "under", in analogy to "over". (ie: x\y = y/x) This appears to generate the sequence A015884.