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

1,2

Links

Table of n, a(n) for n=1..16.

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A108071 A337762 A055876 * A133604 A262345 A192149

Adjacent sequences: A065844 A065845 A065846 * A065848 A065849 A065850

Keyword

base,more,nonn

Author

Sascha Kurz, Nov 24 2001

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

Status

approved