A065852 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).

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, 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, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset: 2

Author

Sascha Kurz, Nov 24 2001

Keywords

• base
• nonn

Comments

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

Examples

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

Crossrefs

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

Programs

Mathematica

c[x_, n_] :=
  Module[{},
   Length[Select[Permutations[x],
     First[#] != 0 && PrimeQ[FromDigits[#, n]] &]]];
A065852[n_] := Module[{i},
   Return[ Max[Map[c[#, n] &, DeleteDuplicatesBy[Tuples[Range[0, n - 1], 3], Table[Count[#, i], {i, 0, n - 1}] &]]]]];
Table[A065852[n], {n, 2, 30}] (* Robert Price, Mar 30 2019 *)

Extensions

Definition corrected by David A. Corneth, Apr 23 2016