Primes with initial digits - errors

[franktaw at netscape.net]

A065584 - A065592 are "Smallest prime beginning with exactly n k's.", 
for k = 1..9.  There appears to be a common error in these sequences.  
The Mathematica code for all of them is similar. While I am not really 
familiar with Mathematica, it appears to me that this code implicitly 
assumes that the digit following the last k is not zero.

I have not checked thoroughly, but at least A065588(10) should be 
5555555555057, not 5555555555129.  (This is the first sequence I looked 
at, and I didn't check any further than this.)

The similar sequences without the "exactly" for k = 1..5 are:

A065584 A068103 A068104 A099658 A068105

These sequences with k = 6..9 do not appear to be in the OEIS.

A068103 and A068104 appear to be correct.  A065584 is definitely wrong; 
a(6) should be 11111101.  A099658 and A068105 appear to be wrong.

It appears that A088639 and A068120 ("Smallest prime beginning with n 
n's.") are essentially the same, except that A068120 has this problem 
(A068120(9) = 99999999943 instead of 99999999907).  a(7) was corrected 
in A068120, but not the rest of the sequence.  I don't know why 
A068120(1) = 13 instead of 11.  (Perhaps it is looking only for numbers 
starting with exactly n n's, although it doesn't say so.  I don't know 
if there is any n > 1 where this makes a difference for this sequence.  
The program appears to be checking for the trailing digits equal to n 
(which always produces a number divisible by n), instead of for 
trailing digits starting with n.)

Could somebody write a correct program, and recompute these sequences?

Franklin T. Adams-Watters

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