OFFSET
2,1
COMMENTS
Contribution R. J. Mathar, May 15 2010 (START):
Supposed all digits are used and the digits at positions 0 to n-1 are d_0, d_1,... d_{n-1}, the candidates are d_0+d_1*n+d_2*n^2+....+d_{n-1}*n^(n-1).
These values are (n-1)*n/2 (mod n-1), and they cannot be prime if n is even, because this number is = 0 (mod n-1) then, showing that n-1 is a divisor.
In conclusion, if n is even, the entries have at most n-1 digits in base n. (END)
If n is odd then the candidate numbers considered in the previous comment are divisible by (n-1)/2. Hence, we conclude that for n>3, a(n) has at most n-1 digits in base n. Conjecture: for n>3, a(n) has exactly n-1 digits in base n. - Eric M. Schmidt, Oct 26 2014
LINKS
Eric M. Schmidt, Table of n, a(n) for n = 2..200
EXAMPLE
a(9) = 42373937 as the prime 42373937 (base 10) = 87654102 (base 9), the largest prime number with distinct digits when represented in base 9.
PROG
(Sage) def a(n) :
if n==2 : return 2
if n==3 : return 19
for P in Permutations(range(n-1, -1, -1), n-1) :
N = sum(P[-1-i]*n^i for i in range(n-1))
if is_prime(N) : return N
# Eric M. Schmidt, Oct 26 2014
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Rick L. Shepherd, Aug 11 2007
EXTENSIONS
Removed my claim of finiteness of the sequence. - R. J. Mathar, May 18 2010
a(11)-a(20) from Eric M. Schmidt, Oct 26 2014
STATUS
approved