(In reply to generalised approach.
Accepting your terminology, let S(n) denote a qualifying number, such that a cubic root of S(n)^3+1 is a smallest positive integer number to produce a result with n zeroes immediately after the decimal point .
So a sequence 2, 6 , 19, 58, 183, 578, 1826, 5777, 18268, 57768 …fits the above description (n - a positive integer).
If we evaluate q(n)= S(n+1)/ S(n) we get 2, 3.1667, 3.0526, 3.1551, ….,3,1622, 3.16225…
It looks like the ratio is closer to sqrt(10), and lim S(n+1)/ S(n) it is likely to be this number.
So the formula SC(n+1)=int ( S(n)*SQRT(10) ) seems more appropriate than yours.
SC- denotes a candidate for S, however IMHO as of 58 and on you get not a candidate, but the true S.
I did not recheck my numbers and if I err, please let me know.
Edited on September 27, 2014, 5:21 am