Re Primes with initial digits - errors: one seq. left to check

[Dan Dima]

I can confirm these results. Some more terms:

21212121212121212121212121212121212121212119
2222222222222222222222222222222222222222222297
232323232323232323232323232323232323232323232361
242424242424242424242424242424242424242424242424293
25252525252525252525252525252525252525252525252525061
2626262626262626262626262626262626262626262626262626003
2727272727272727272727272727272727272727272727272727271
28282828282828282828282828282828282828282828282828282828057
292929292929292929292929292929292929292929292929292929292907
303030303030303030303030303030303030303030303030303030303030043
3131313131313131313131313131313131313131313131313131313131313161
3232323232323232323232323232323232323232323232323232323232323232007
333333333333333333333333333333333333333333333333333333333333333333053
3434343434343434343434343434343434343434343434343434343434343434343431
3535353535353535353535353535353535353535353535353535353535353535353535127


I think we can conjecture that A068120 is a strictly increasing sequence...

An interesting subsequence of this might be that one that has exactly one
extra digit appended...

Meanwhile I think that A088639 is redundant since A088639(n)=A068120(n).

A068008 is somehow tricky if we consider leading 0's:
A068008(25)=153
but:
25252525252525252525252525252525252525252525252525061
is a smaller prime than:
25252525252525252525252525252525252525252525252525163
A068008(26)=163
 but:
2626262626262626262626262626262626262626262626262626003
is a smaller prime than:
2626262626262626262626262626262626262626262626262626163


Best regards,
Dan Dima









On 1/27/07, Jacques Tramu <jacques.tramu at echolalie.com> wrote:
>
>
>
> >From: "N. J. A. Sloane" <njas at research.att.com>
> > could someone please check it?  Here is the current entry:
>
> >
> > %I A068120
> > %S A068120
> > 13,223,3331,44449,555557,66666629,777777701,888888883,99999999907,
> > %T A068120 1010101010101010101039,11111111111111111111111,
> > %U A068120 12121212121212121212121223,1313131313131313131313131327
> > %N A068120 Smallest prime beginning with exactly n n's.
> > %K A068120 base,easy,nonn,new
> > %O A068120 1,1
> > %A A068120 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 21 2002
> > %E A068120 Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com),
> > Feb 22 2002
> > %E A068120 a(7) corrected by Amarnath Murthy
> > (amarnath_murthy(AT)yahoo.com), Mar 24 2002
> > %E A068120 Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 14 2006
> >
>
> Here are my results  + some new entries -  different entry  is flagged (*)
>
> 13 , 223, 3331, 44449, 555557, 66666629, 777777701, 888888883,
> 99999999907,
> 1010101010101010101039, 11111111111111111111111,
> 12121212121212121212121223, *1313131313131313131313131301*,
> 141414141414141414141414141497, 15151515151515151515151515151501,
> 1616161616161616161616161616161691, 171717171717171717171717171717171737,
>
> 181818181818181818181818181818181818059,1919191919191919191919191919191919191909,
> 202020202020202020202020202020202020202093
>
> regards,
> JT
>
>
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