[seqfan] Re: Primes adding one of their digit to themselves (+chains)

[M. F. Hasler]

See also :
oeis.org/A048519 : Prime plus its digit sum equals a prime.
subsequence of
oeis.org/A047791 : Numbers n such that n plus digit sum of n (A007953)
equals a prime.
and references therein (self numbers, ...).

M.

On Thu, Aug 7, 2014 at 7:36 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
> Hello SeqFans,
> Paolo Lava has computed 1000 terms of S - many thanks to him
> (I hope that the seq will be accepted in the OEIS if of interest)
>
> [Reminder: all terms are primes; if you add to the term a(n)
> one of its digits, you'll get another prime; example 29+2=31
> or 43+4=47 or 61+6=67]
>
> S = 29, 43, 61, 67, 89, 167, 227, 239, 263, 269, 281, ...
> The "chains" have also a certain charm, no? Paolo computed a few
> of those - and I think that the first term of each line could also
> produce a nice seq.
>
> [Reminder: to jump from one prime 'p' to the next one in the "chain",
> add to 'p' one of its digits]
> PL> first chains of 4 terms:
>
>    601 -> 607 -> 613 -> 619
>
> PL> first chains of 5 terms:
>     6257 -> 6263 -> 6269 -> 6271 -> 6277
> PL> first chains of 6 terms:
>     19417 -> 19421 -> 19423 -> 19427 -> 19429 -> 19433
> PL> and so on... Here the first chain with 10 primes:
>     246899 -> 246907 -> 246913 -> 246919 -> 246923 -> 246929 -> 246931 -> 246937 -> 246941 -> 246947
> Bravo, Paolo!
>
> ------------
> Now, what about alternating primes 'p' and non-primes 'q'?
>
> Starting with a 'p', we have this 10-element alternating "chain",
> for instance:
>
>
> T = 5-10-11-12-13-16-17-18-19-28 END
>
>     p  q  p  q  p  q  p  q  p  q
>
>
>
> As always, the difference 'd' between two terms a(n) and a(n+1)
>
> must be one of the digits of a(n).