A065852 - OEIS

%I #20 Jun 24 2024 15:31:40

%S 1,2,3,4,4,5,3,5,4,6,4,6,4,5,5,5,4,6,5,6,5,6,5,6,5,6,5,6,5,6,5,6,6,6,

%T 6,6,5,6,6,6,5,6,6,6,6,5,5,6,6,6,6,6,5,6,6,6,5,6,6,6,6,6,6,6,6,6,5,6,

%U 6,6,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6

%N Let u be any string of 3 digits from {0,...,n-1}; let f(u) = number of distinct primes, not beginning with 0, formed by permuting the digits of u to a base-n number; then a(n) = max_u f(u).

%C a(n) = 6 for 73 <= n < 985, except a(192) = 5.

%e a(2)=1 because 101 is prime and there are no two 3-digit primes with the same number of ones in base two.

%t c[x_, n_] :=

%t   Module[{},

%t    Length[Select[Permutations[x],

%t      First[#] != 0 && PrimeQ[FromDigits[#, n]] &]]];

%t A065852[n_] := Module[{i},

%t    Return[ Max[Map[c[#, n] &, DeleteDuplicatesBy[Tuples[Range[0, n - 1], 3], Table[Count[#, i], {i, 0, n - 1}] &]]]]];

%t Table[A065852[n], {n, 2, 30}] (* _Robert Price_, Mar 30 2019 *)

%Y Cf. A065843, A065844, A065845, A065846, A065847, A065848, A065849, A065850, A065851, A065853.

%K base,nonn

%O 2,2

%A _Sascha Kurz_, Nov 24 2001

%E Definition corrected by _David A. Corneth_, Apr 23 2016