%C A136296 "Special augmented numbers" from Zak Seidov

[franktaw at netscape.net]

No, that was my error; I didn't go look, so I didn't realize that 
A136296 was
restricted to only prime values.

Up to 60 digits, A136296 is:

11, 13, 137, 9091, 909091, 5882353, 909090909090909091,
909090909090909090909090909091,
9090909090909090909090909090909090909090909090909091

(Some of these may be only probable primes; I just used PARI's factor
function.)

The values I supplied before are actually A116436.

(Incidentally, up to 40 digits, A116436 is:

1, 11, 13, 77, 91, 137, 9091, 909091, 5882353, 10989011,
12987013, 52631579, 76923077, 90909091, 4347826087,
9090909091, 13698630137, 909090909091, 3448275862069,
10989010989011, 12987012987013, 76923076923077,
90909090909091, 9090909090909091, 909090909090909091,
1369863013698630137, 10989010989010989011,
12987012987012987013, 20408163265306122449,
76923076923076923077, 90909090909090909091,
112359550561797752809, 2127659574468085106383,
9090909090909090909091, 58823529411764705882353,
909090909090909090909091, 10989010989010989010989011,
12987012987012987012987013, 52631578947368421052631579,
76923076923076923076923077, 90909090909090909090909091,
136986301369863013698630137,
1694915254237288135593220339,
9090909090909090909090909091,
16393442622950819672131147541,
909090909090909090909090909091,
10989010989010989010989010989011,
12987012987012987012987012987013,
43478260869565217391304347826087,
76923076923076923076923076923077,
90909090909090909090909090909091,
9090909090909090909090909090909091,
13698630136986301369863013698630137,
909090909090909090909090909090909091,
10989010989010989010989010989010989011,
12987012987012987012987012987012987013,
76923076923076923076923076923076923077,
90909090909090909090909090909090909091,
588235294117647058823529411764705882353,
9090909090909090909090909090909090909091

This takes only a few seconds, so it could be extended easily enough.)

Here's PARI code for A136296:

A136296k(k) = {
 local(l, d, lb, ub);
 d=factor(10^(k+1)+1)[,1];
 l=[];
 lb=10^(k-1);
 ub=10*lb;
 for(i=1,#d,if(d[i]>=lb&&d[i]<ub,l=concat(l,[d[i]])));
 l}

And then

l=[];for(i=1,60,l=concat(l,A136296k(i)));l

gives the values shown above.

I have submitted comments for both of these sequences with the 
additional values,
cross-references, and the PARI programs.  I also included Zak's 
original comment,

Notice the infinite pattern
p=(90..90..90)91 with 1p1/p=21, e.g.,
1911/91=190911/9091=19090911/909091=21.

but as a comment for A116436 instead of for A136296 (and with "p" 
replaced by "n").
(I gave him attribution for this, of course.)

Franklin T. Adams-Watters

-----Original Message-----
From: Alexander Povolotsky <apovolot at gmail.com>

Thanks Richard -

- but I was hoping that someone would also find at least one (first
that is) occurence of such intersection,
if such intersection does indeed occurs - so far (among 40 or or so
terms ;-) )
I see that terms in both seqs are the same (or did I overlook the
difference which  is present in already posted terms ?).

> ap> A116436  =
> ap> 1, 11, 13, 77, 91, 137, 9091, 909091, 5882353, 10989011, 12987013,
> ap> 52631579, 76923077, 90909091, 4347826087, 9090909091, 13698630137,
> ap> 909090909091, 3448275862069, 10989010989011, 12987012987013,
> ap> 76923076923077

A136296(k) =
1, 11, 13, 77, 91, 137, 9091, 909091, 5882353, 10989011,
12987013, 52631579, 76923077, 90909091, 4347826087,
9090909091, 13698630137, 909090909091, 3448275862069,
10989010989011, 12987012987013, 76923076923077,
90909090909091, 9090909090909091, 909090909090909091,
1369863013698630137, 10989010989010989011,
12987012987012987013, 20408163265306122449,
76923076923076923077, 90909090909090909091

Franklin T. Adams-Watters