A065847 Let u be any string of n digits from {0,...,5}; let f(u) = number of distinct primes, not beginning with 0, formed by permuting the digits of u to a base-6 number; then a(n) = max_u f(u).

1, 2, 4, 8, 21, 60, 269, 1147, 4250, 17883, 71966, 342060, 1724337, 8428101, 37186164, 175845403

Offset: 1

Author

Sascha Kurz, Nov 24 2001

Keywords

• base
• more
• nonn

Examples

			a(2)=2 because 15 and 51 (written in base 6) are primes (11 and 31).
		

Crossrefs

Cf. A065843, A065844, A065845, A065846, A065848, A065849, A065850, A065851, A065852, A065853.

Programs

Maple

A065847 := proc(n)
    local b,u,udgs,uperm,a;
    b :=6 ;
    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,A065847(n)) ;
end do: # R. J. Mathar, Apr 23 2016

Mathematica

c[x_] := Module[{},
   Length[Select[Permutations[x],
     First[#] != 0 && PrimeQ[FromDigits[#, 6]] &]]];
A065847[n_] := Module[{i},
   Return[Max[Map[c, DeleteDuplicatesBy[Tuples[Range[0, 5], n],
       Table[Count[#, i], {i, 0, 5}] &]]]]];
Table[A065847[n], {n, 1, 8}] (* Robert Price, Mar 30 2019 *)

Python

from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
from itertools import combinations_with_replacement
def A065847(n):
    return max(sum(1 for t in multiset_permutations(s) if t[0] != '0' and isprime(int(''.join(t),6))) for s in combinations_with_replacement('012345',n)) # Chai Wah Wu, Apr 23 2019

Extensions

a(12)-a(13) from Sean A. Irvine, Sep 06 2009

Definition corrected by David A. Corneth, Apr 23 2016

a(14) from Chai Wah Wu, Jun 15 2019

a(15) from Michael S. Branicky, Jun 25 2024

a(16) from Michael S. Branicky, Jul 02 2024