A065845 Let u be any string of n digits from {0,...,3}; let f(u) = number of distinct primes, not beginning with 0, formed by permuting the digits of u to a base-4 number; then a(n) = max_u f(u).

1, 2, 3, 6, 13, 36, 96, 253, 765, 2683, 7385, 25075, 83150, 293063, 888689, 3161645, 11097301, 40328876, 129951350, 469528189, 1694632516

Offset: 1

Author

Sascha Kurz, Nov 24 2001

Keywords

• base
• more
• nonn

Examples

			a(2)=2 because 13 and 31 (written in base 4) are primes (7 and 13).
		

Crossrefs

Cf. A065843, A065844, A065846, A065847, A065848, A065849, A065850, A065851, A065852, A065853

Programs

Maple

A065845 := proc(n)
    local b,u,udgs,uperm,a;
    b :=4 ;
    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,A065845(n)) ;
end do: # R. J. Mathar, Apr 23 2016

Mathematica

c[x_] := Module[{},
   Length[Select[Permutations[x],
     First[#] != 0 && PrimeQ[FromDigits[#, 4]] &]]];
A065845[n_] := Module[{i},
   Return[Max[Map[c, DeleteDuplicatesBy[Tuples[Range[0, 3], n],
       Table[Count[#, i], {i, 0, 3}] &]]]]];
Table[A065845[n], {n, 1, 10}] (* Robert Price, Mar 30 2019 *)

Extensions

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

Definition corrected by David A. Corneth, Apr 23 2016

a(19) from Michael S. Branicky, May 29 2024

a(20)-a(21) from Michael S. Branicky, Jun 14 2024