non-standard sieve

[req]

I want to sieving the numbers (b^n+-k)/p
where
k- fixed
p- divisor, fixed

for exemple numbers
3333....331
represented by the formula
(10^n-7)/3

Repunit
11111...11
(10^n-1)/9

2 questions:

1.what program is there?
NewPgen similar, but only for b^n+-k, k- fixed

2.how to quickly find the smallest n0
b^n0 = k mod p
after we eliminate the fast
n0, n0 + p-1, n0 + 2(p-1).....

[axn]

Originally Posted by req

1.what program is there?
NewPgen similar, but only for b^n+-k, k- fixed

You can use NewPGen itself to do the sieve. However, you have to manually create an initial sieve file with all the n's you want (use a script). Then set the header to use a composite that is just 1 above the largest factor of your "p". The use NewPGen to "continue sieving". It will continue to sieve with all the primes > "p".

For example, I created a file like so, for 10^n-7.

4:M:0:10:32770
7 20
7 21
7 22
7 23
7 24
7 25
7 26
7 27
7 28
7 29
7 30
7 31
7 32
7 33
7 34
7 35
7 36
7 37
7 38
7 39
7 40
7 41
7 42
7 43
7 44
7 45
7 46
7 47
7 48

[req]

Thank you very much, this is a good solution.
It is true, then again to make a script to:
4:M:0:10:32770
7 18
7 19
7 20
7 21
7 22
7 23
7 24

that will remain after sieving
for PFGW in:
(10^18 - 7)/3
(10^24 - 7)/3
....

I think it's easy to write in the program. Because the algorithm is unchanging, but the only change formats

[req]

Note.
This idea makes it easy to parallelize sieving. Quickly weed out the major candidates n <10^9, and then make the files of the form, exemple:
file1:
1000000000: M: 0:10:32770
check up to 2*10^10

file2:
2000000000: M: 0:10:32770
check up to 3*10^10

file3:
3000000000: M: 0:10:32770
check up to 4*10^10

file4:
4000000000: M: 0:10:32770
check up to 5*10^10
....
Compare the files and find duplicate value. To generate the output file.

[axn]

Originally Posted by req

Note.
This idea makes it easy to parallelize sieving. Quickly weed out the major candidates n <10^9, and then make the files of the form, exemple:
file1:
<snip>
Compare the files and find duplicate value. To generate the output file.

NewPGen has this option also! From "Services" menu, you have "Duplicate" and "Merge" options which perform exactly these things.