[seqfan] Primes, concats and videotapes

[Eric Angelini]

[This message of mine never appeared on SeqFans,
 here is a duplicate]

                       -----Message d'origine-----
                       De : Eric Angelini 
                       Envoyé : lundi 22 novembre 2010 16:08
                       À : 'Seqfan Mailing List'
                       Objet : Primes, concats and videotapes
Hello SeqFans,

Three thingies:

Let:
a(1) = 1
a = a(n)
b = a(n+1)
b>a
d = b-a
[t,u,...,z] = the concatenation of the strings
              't' and 'u' and ... and 'z'

Now build S(1) where b is the smallest integer such
               that [a,d] is prime

... build S(2) where b is the smallest integer such
               that [d,b] is prime 

... build S(3) where b is the smallest integer such
               that [a,d,b] is prime 

Are the herunder starts correct?

S(1) = 1, 2, 5, 8, 11, 14, 23, 26, 29, 32,  49, ...
   d =   1  3  3  3   3   9   3   3   3   17
   p =  11,23,53,83,113,149,233,263,293,3217,

S(2) = 1, 3, 7, 9, 11, 17, 21, 23,  33,  47, 53, ...
   d =   2  4  2  2   6   4   2   10   14   6
   p =   23,47,29,211,617,421,223,1033,1447,653,

S(3) = 1,  7,   11,   13,   17,   23,   29,   31,  41, ...
   d =   6    4    2     4     6     6      2    10
   p =  167,7411,11213,13417,17623,23629,29231,311041,
          
Best,
É.