

A334885


Let q = p  p' be the digit concatenation of a prime p with its prime successor. If the result is a prime repeat the construction setting p = q. a(n) is the smallest prime for which this can be repeated exactly n times.


0




OFFSET

0,1


COMMENTS

a(6) > 10^13.


LINKS



EXAMPLE

Let "" denote concatenation.
3  5 = 35, which is not prime, so a(0) = 3.
2  3 = 23 (prime), 23  29 = 2329 (composite), so a(1) = 2.
13681  13687 (prime), 1368113687  1368113699 (prime), 13681136871368113699  13681136871368113711 (composite), so a(2) = 13681.


MATHEMATICA

a[n_] := Block[{pp=1, p, q, c=1}, While[ c!=n, c=0; p = pp = NextPrime@ pp; While[ PrimeQ[ q = FromDigits[ Join @@ IntegerDigits@{p, NextPrime@ p}]], c++; p = q]]; pp]; a /@ Range[0, 3]


CROSSREFS



KEYWORD

nonn,base,more


AUTHOR



STATUS

approved



