Primes with initial digits - errors

[Don Reble]

> 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 ... it appears to me that this code implicitly 
> assumes that the digit following the last k is not zero.

    Also, the single-digit primes are missing.

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

    Ok.

%S A065584 13,11,1117,11113,111119,11111101,11111117,111111113,11111111129,
%T A065584 11111111113,1111111111139,11111111111123,1111111111111013,
%U A065584 1111111111111123,11111111111111101,11111111111111119

%S A065585 2,223,2221,22229,2222203,22222253,22222223,222222227,22222222273,
%T A065585 22222222223,2222222222243,22222222222201,22222222222229,
%U A065585 222222222222227,222222222222222043,222222222222222281

%S A065586 3,331,3331,33331,333331,3333331,33333331,3333333319,33333333329,
%T A065586 333333333323,3333333333301,33333333333319,333333333333307,
%U A065586 3333333333333301,33333333333333323,333333333333333391

%S A065587 41,443,4441,44449,444443,44444453,444444421,444444443,4444444447,
%T A065587 44444444441,444444444443,44444444444459,444444444444421,
%U A065587 4444444444444423,44444444444444411,444444444444444413

%S A065588 5,557,5557,555521,555557,55555517,55555553,5555555501,5555555557,
%T A065588 5555555555057,555555555551,5555555555551,555555555555529,
%U A065588 555555555555557,55555555555555519,5555555555555555021

%S A065589 61,661,6661,666607,666667,66666629,66666667,666666667,6666666661,
%T A065589 66666666667,6666666666629,66666666666629,666666666666631,
%U A065589 66666666666666047,66666666666666601,6666666666666666059

%S A065590 7,773,77711,77773,7777709,77777719,777777701,777777773,77777777717,
%T A065590 777777777713,777777777773,7777777777771,777777777777719,
%U A065590 777777777777773,77777777777777711,777777777777777737

%S A065591 83,881,8887,88883,888887,88888817,88888883,888888883,88888888801,
%T A065591 888888888859,888888888887,88888888888873,88888888888889,
%U A065591 888888888888883,88888888888888801,88888888888888889

%S A065592 97,991,99901,99991,9999901,9999991,999999929,9999999929,99999999907,
%T A065592 999999999937,9999999999971,99999999999923,999999999999947,
%U A065592 9999999999999917,99999999999999919,99999999999999997

    I agree with only A065587. I hope that someone who knows Mathematica
    will edit. (I guess that even the A065587 code is wrong.)


> The similar sequences without the "exactly" for k = 1..5 are:
> A065584 A068103 A068104 A099658 A068105

> A068103 and A068104 appear to be correct.
    Wait a minute: if A068103(6) = 22222223, why doesn't A068103(0) = 2?
    But I agree with the rest of the A068103 and all of A068104. A068105
    is wrong.

%S A068105 2,5,557,5557,555521,555557,55555517,55555553,5555555501,5555555557,
%T A068105 555555555551,555555555551,5555555555551,555555555555529,
%U A068105 555555555555557,55555555555555519,555555555555555559

    A099658 is a different kind of sequence.

-- 
Don Reble  djr at nk.ca


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