A065846 Let u be any string of n digits from {0,...,4}; let f(u) = number of distinct primes, not beginning with 0, formed by permuting the digits of u to a base-5 number; then a(n) = max_u f(u).

1, 2, 4, 7, 26, 87, 226, 800, 2424, 9975, 40045, 152852, 626232, 2317403, 9962949, 43599477, 179247754, 777881238

Offset

1,2

Links

Table of n, a(n) for n=1..18.

Example

a(2)=2 because 12 and 21 (written in base 5) are primes (7 and 11).

Maple

A065846 := proc(n)
    local b, u, udgs, uperm, a;
    b :=5 ;
    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, A065846(n)) ;
end do: # R. J. Mathar, Apr 23 2016

Mathematica

c[x_] := Module[{},
   Length[Select[Permutations[x],
     First[#] != 0 && PrimeQ[FromDigits[#, 5]] &]]];
A065846[n_] := Module[{i},
   Return[Max[Map[c, DeleteDuplicatesBy[Tuples[Range[0, 4], n],
       Table[Count[#, i], {i, 0, 4}] &]]]]];
Table[A065846[n], {n, 1, 9}] (* Robert Price, Mar 30 2019 *)

Crossrefs

Cf. A065843, A065844, A065845, A065847, A065848, A065849, A065850, A065851, A065852, A065853.

Sequence in context: A222907 A179386 A343977 * A242020 A047904 A102118

Adjacent sequences: A065843 A065844 A065845 * A065847 A065848 A065849

Keyword

base,more,nonn

Author

Sascha Kurz, Nov 24 2001

Extensions

2 more terms from Sean A. Irvine, Sep 06 2009

Definition corrected by David A. Corneth, Apr 23 2016

a(16) from Michael S. Branicky, May 29 2024

a(17) from Michael S. Branicky, Jun 26 2024

a(18) from Michael S. Branicky, Jul 08 2024

Status

approved