A139074 or 0 if no such prime exists.

[Richard Mathar]

Definitely, this morning I'm a bit dizzy...
I agree that your code is much more intelligent.
(but the existing sequences only lists primes, so "divisors" should be
replaced by "factor()[,1]" ;
also I don't think there can be more than the largest and second
largest in the prime factors to have the required number of digits)
Maximilian


On Tue, Apr 22, 2008 at 11:06 AM,  <franktaw at netscape.net> wrote:
> This is not so difficult.  We're looking for k digit numbers that divide
>  10^{k+1}+1.  (Anybody not see why this is equivalent?)
>
>  Some PARI:
>
>  A136296k(k) = {local(l, d, lb, ub);
>  d=divisors(10^(k+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}
>
>  l=[];for(i=1,20,l=concat(l,A136296k(i)));l
>
>  And we get:
>
>  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
>
>
>
>  -----Original Message-----
>  From: Maximilian Hasler <maximilian.hasler at gmail.com>
>
>  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:
> >
> >
>  1,11,13,77,91,137,9091,909091,90909091,9090909091,909090909091,9090909090
>  9091,9090909090909091,909090909090909091.
>
> >  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
> >
>
>
>
>
>
>