OFFSET
1,2
COMMENTS
a(25) >= 1325189141 via permutations of numbers with eight 0's, nine 1's and eight 2's. If some permutation class gives a larger number of primes then it's smallest element is lexicographically larger than 1000000001111111111111222. Permutation class 1000000011111111222222222 gives fewer primes than 1325189141. - David A. Corneth, May 31 2024
EXAMPLE
a(2)=2 because 12 and 21 (written in base 3) are primes (5 and 7).
MAPLE
A065844 := proc(n)
local b, u, udgs, uperm, a;
b :=3 ;
a := 0 ;
for u from b^(n-1) to b^n-1 do
udgs := convert(u, base, b) ;
prs := {} ;
for uperm in combinat[permute](udgs) do
if op(-1, uperm) <> 0 then
p := add( op(i, uperm)*b^(i-1), i=1..nops(uperm)) ;
if isprime(p) then
prs := prs union {p} ;
end if;
end if;
end do:
a := max(a, nops(prs)) ;
end do:
a ;
end proc:
for n from 1 do
print(n, A065844(n)) ;
end do: # R. J. Mathar, Apr 23 2016
MATHEMATICA
c[x_] := Module[{},
Length[Select[Permutations[x],
First[#] != 0 && PrimeQ[FromDigits[#, 3]] &]]];
A065844[n_] := Module[{i},
Return[Max[Map[c, DeleteDuplicatesBy[Tuples[Range[0, 2], n],
Table[Count[#, i], {i, 0, 2}] &]]]]];
Table[A065844[n], {n, 1, 13}] (* Robert Price, Mar 30 2019 *)
CROSSREFS
KEYWORD
base,nonn,more
AUTHOR
Sascha Kurz, Nov 24 2001
EXTENSIONS
3 more terms from Sean A. Irvine, Sep 06 2009
Definition corrected by David A. Corneth, Apr 23 2016
a(23)-a(24) from Michael S. Branicky, May 30 2024
a(25) confirmed by Michael S. Branicky, Jun 03 2024
a(26) from Michael S. Branicky, Jun 08 2024
a(27) from Michael S. Branicky, Jun 23 2024
STATUS
approved