(In reply to

generalised approach. by broll)

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**