[seqfan] Re: Number of primes having distinct first and last digits both 7 to 10^n primes

Jack Brennen jfb at brennen.net
Mon Aug 2 23:07:24 CEST 2010


Yeah, it's better defined as:  out of the first 10^n primes,
the count of those which are at least two digits long and
which begin and end with the digit 7.

It's definitely not "easy", since we don't really have the
computing power to compute even 25 terms of the sequence.

Also, the offset shouldn't be 3; the way it's written, the
proper offset would be 1, although I think it should likely
be offset=0, because the sequence is well defined for n=0.

With the offset set to zero, I get:

   0, 0, 0, 32, 264, 2103, 17891, 155956, ...



Charles Greathouse wrote:
> A145711 is defined as "Number of primes having distinct first and last
> digits both 7 to 10^n primes".  It seems to mean something similar to
> "Number of primes below 10^n with distinct first and last decimal
> digits", but this isn't quite it.  Can anyone decipher it?
> 
>>From its description:
> Comment: The first prime with equal first and last digits is 11 -- the
> two digits must be distinct, so 7, for example, cannot be
> double-counted.
> Example: a(3)=32 because to 10^3 or 1000 primes, ending in 7919, there
> are 32 primes with equal and distinct first and last digits: 7 and 7.
> 
> It also needs keyword work: it needs "base" but not "easy" (since it
> involves exponentially many terms).
> 
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
> 
> 
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> 
> 





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