[seqfan] Re: A090709 Decimal primes whose decimal representation in base 6 is also prime.

[M. F. Hasler]

Many corrections and (I hope) improvements have been made (or are in
course / draft) to A090707 - A091924 and others not in this range
(b=2,3) and their "reciprocals", thanks to Veikko Pohjola's initial
and subsequent observations, and other suggestions by Donovan Johnson,
Joerg Arndt and Charles Greathouse (and maybe others, apolgies for
undue omissions).

It would be nice if s/o could compile a table / list of these
sequences and their "reciprocals" that would allow an easy quick
reference to all of these:

base b: 2,3,4,....,1024
Primes whose base-b representation is the base-10 representation of a
prime: Axxx, Ayyy,....
Primes whose base-10 representation is the base-b representation of a
prime: Azzz, Attt

Other couples than (b,10) and (10,b) are possible and maybe are or
should be(?) in OEIS:

is(p,b=2,c=3)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)
forprime(p=1,999,is(p)&print1(p","))
3,13,31,37,271,283,733,757,769,

=> These are primes whose base 3 representation also is the base-2
representation of a prime.
(e.g. 3 = 10[3] and 10[2] = 2 is prime ; 13 = 111[3] and 111[2] = 7 is
prime ; ...)

Without being a fanatic of "base" sequences, I think for small b,c
(e.g. all < 10 and/or primes < 20) these could or should be included,
for the sake of encyclopaedic completeness of OEIS.

That said, I just decided to submit the above as https://oeis.org/draft/A235265.

Maximilian

On Fri, Jan 3, 2014 at 5:10 AM, Veikko Pohjola <veikko at nordem.fi> wrote:
> Dear seqfans,
>
> A090709 lists the numbers which are obtained by converting first all (decimal) primes into base 6 and then keeping those whose digits make a decimal prime. The title of the sequence is "Decimal primes whose decimal representation in base 6 is also prime". Maybe I misunderstand what the title says, but I would expect the sequence to be composed of those decimal primes, which after conversion yield the appropriate digits, but not the primes which the digits make.
>
> The example given by the author tells that  "19 is prime in decimal and 19 base 6 is 31, which is also prime in decimal". I would thus expect 19 to be the prime that the title refers to rather than 31. Hereby the title, as it is written, would actually refer to A065724 titled "Primes p such that the decimal representation of its base 6 conversion is also prime". The example given for  A065724 is formally identical with the example above: "19(10) = 31(6) is prime but also 31(10)".
>
> Should the title of A090709 be deciphered or is it only my insufficient English which is the problem here?
> Veikko
>
>
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-- 
Maximilian