A139074 or 0 if no such prime exists.

[drew at math.mit.edu]

1p1 divisible by p
<=> 10^[log10(p)+2] + 10p + 1 divisible by p
<=> 10^[log10(p)+2] + 1 divisible by p
<=> 10^[log10(p)+2] = -1 (mod p)

Three more terms ; a(7)>10^7.

%I A136296
%S A136296 11, 13, 137, 9091, 909091, 5882353
%F A136296 1p1 divisible by p <=> 10^[log[10](p)+2] = -1 (mod p)
%o A136296 (PARI) forprime(p=1,10^7,Mod(10,p)^(log(p)\log(10)+2)+1 |
print1(p", "))
%A A136296 M. F. Hasler (Maximilian.Hasler at gmail.com), Apr 22 2008


On Tue, Apr 22, 2008 at 1:24 AM, zak seidov <zakseidov at yahoo.com> wrote:
> %C A136296 "Special augmented numbers"  p such that
>  the decimal number 1p1 is divisible by p:
>  1,11,13,77,91,137,9091,909091,90909091,9090909091,909090909091,90909090909091,9090909090909091,909090909090909091.
>  Notice the infinite pattern
>  p=(90..90..90)91 with 1p1/p=21, e.g.,
>  1911/91=190911/9091=19090911/909091=21.
>
>  Prime numbers are
>  11, 13, 137, 9091, 909091, 909090909090909091