IF statement to evaluate result of random number generator to generate next random number

I need to scan for random account numbers through a sheet containing account numbers and their details. I have used the following formula to do this:

Formula:

=INDEX(RETRENCHMENT!A:A,RANDBETWEEN(2,COUNTA(RETRENCHMENT!A:A)),1)

The catch is that column A of the sheet, which contains the account numbers, also contains blank cells between account numbers, and the account numbers are not evenly spaced from each other, and I require the formula to return only account numbers and not blank cells.

My solution to this has been to try to evaluate the result of the INDEX-RANDBETWEEN formula above using an IF statement in order to decide whether I want to try run the formula again so that I can get a different result.

I have used:

Formula:

=IF(INDEX(RETRENCHMENT!A:A,RANDBETWEEN(2,COUNTA(RETRENCHMENT!A:A)),1)="",IF(INDEX(RETRENCHMENT!A:A,RANDBETWEEN(3,COUNTA(RETRENCHMENT!A:A)),1),IF(INDEX(RETRENCHMENT!A:A,RANDBETWEEN(2,COUNTA(RETRENCHMENT!A:A)),1))

In the THEN condition of the IF statement I changed the RANDBETWEEN range to start on the third row to try and "force" a new random process from occuring (not sure if this is necessary). I have gone on to nest this process as far as probabilistically sufficient in my mind but the formula seems still to return a disproportionate number of blank results, leading me to believe that nesting these functions like this does not force Excel to try a different random cell on the RETRENCHMENT sheet.

My end result of nesting was this:

Formula:

=IF(INDEX(RETRENCHMENT!A:A,RANDBETWEEN(2,COUNTA(RETRENCHMENT!A:A)),1)="",IF(INDEX(RETRENCHMENT!A:A,RANDBETWEEN(3,COUNTA(RETRENCHMENT!A:A)),1)="",IF(INDEX(RETRENCHMENT!A:A,RANDBETWEEN(4,COUNTA(RETRENCHMENT!A:A)),1)="",IF(INDEX(RETRENCHMENT!A:A,RANDBETWEEN(6,COUNTA(RETRENCHMENT!A:A)),1)="",IF(INDEX(RETRENCHMENT!A:A,RANDBETWEEN(6,COUNTA(RETRENCHMENT!A:A)),1)="",IF(INDEX(RETRENCHMENT!A:A,RANDBETWEEN(7,COUNTA(RETRENCHMENT!A:A)),1)="",IF(INDEX(RETRENCHMENT!A:A,RANDBETWEEN(8,COUNTA(RETRENCHMENT!A:A)),1)="",IF(INDEX(RETRENCHMENT!A:A,RANDBETWEEN(9,COUNTA(RETRENCHMENT!A:A)),1)="",IF(INDEX(RETRENCHMENT!A:A,RANDBETWEEN(10,COUNTA(RETRENCHMENT!A:A)),1)="",IF(INDEX(RETRENCHMENT!A:A,RANDBETWEEN(11,COUNTA(RETRENCHMENT!A:A)),1)="",INDEX(RETRENCHMENT!A:A,RANDBETWEEN(12,COUNTA(RETRENCHMENT!A:A)),1),INDEX(RETRENCHMENT!A:A,RANDBETWEEN(11,COUNTA(RETRENCHMENT!A:A)),1)),INDEX(RETRENCHMENT!A:A,RANDBETWEEN(10,COUNTA(RETRENCHMENT!A:A)),1)),INDEX(RETRENCHMENT!A:A,RANDBETWEEN(9,COUNTA(RETRENCHMENT!A:A)),1)),INDEX(RETRENCHMENT!A:A,RANDBETWEEN(8,COUNTA(RETRENCHMENT!A:A)),1)),INDEX(RETRENCHMENT!A:A,RANDBETWEEN(7,COUNTA(RETRENCHMENT!A:A)),1)),INDEX(RETRENCHMENT!A:A,RANDBETWEEN(6,COUNTA(RETRENCHMENT!A:A)),1)),INDEX(RETRENCHMENT!A:A,RANDBETWEEN(5,COUNTA(RETRENCHMENT!A:A)),1)),INDEX(RETRENCHMENT!A:A,RANDBETWEEN(4,COUNTA(RETRENCHMENT!A:A)),1)),INDEX(RETRENCHMENT!A:A,RANDBETWEEN(3,COUNTA(RETRENCHMENT!A:A)),1)),INDEX(RETRENCHMENT!A:A,RANDBETWEEN(2,COUNTA(RETRENCHMENT!A:A)),1))

Is there a more efficient way (and that works) of letting Excel perform a random number generation, having it evaluate the result of this process and then based on this result either return the result or re-run the random number generation to return a different result?