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

2,2

Comments

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

Links

Table of n, a(n) for n=2..88.

Example

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

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 *)

Crossrefs

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

Sequence in context: A353948 A334049 A058277 * A303998 A319712 A319715

Adjacent sequences: A065849 A065850 A065851 * A065853 A065854 A065855

Keyword

base,nonn

Author

Sascha Kurz, Nov 24 2001

Extensions

Definition corrected by David A. Corneth, Apr 23 2016

Status

approved