A065846 - OEIS

%I #31 Jul 08 2024 10:38:58

%S 1,2,4,7,26,87,226,800,2424,9975,40045,152852,626232,2317403,9962949,

%T 43599477,179247754,777881238

%N 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).

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

%p A065846 := proc(n)

%p     local b,u,udgs,uperm,a;

%p     b :=5 ;

%p     a := 0 ;

%p     for u from b^(n-1) to b^n-1 do

%p         udgs := convert(u,base,b) ;

%p         prs := {} ;

%p         for uperm in combinat[permute](udgs) do

%p             if op(-1,uperm) <> 0 then

%p                 p := add( op(i,uperm)*b^(i-1),i=1..nops(uperm)) ;

%p                 if isprime(p) then

%p                     prs := prs union {p} ;

%p                 end if;

%p             end if;

%p         end do:

%p         a := max(a,nops(prs)) ;

%p     end do:

%p     a ;

%p end proc:

%p for n from 1 do

%p     print(n,A065846(n)) ;

%p end do: # _R. J. Mathar_, Apr 23 2016

%t c[x_] := Module[{},

%t    Length[Select[Permutations[x],

%t      First[#] != 0 && PrimeQ[FromDigits[#, 5]] &]]];

%t A065846[n_] := Module[{i},

%t    Return[Max[Map[c, DeleteDuplicatesBy[Tuples[Range[0, 4], n],

%t        Table[Count[#, i], {i, 0, 4}] &]]]]];

%t Table[A065846[n], {n, 1, 9}] (* _Robert Price_, Mar 30 2019 *)

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

%K base,more,nonn

%O 1,2

%A _Sascha Kurz_, Nov 24 2001

%E 2 more terms from _Sean A. Irvine_, Sep 06 2009

%E Definition corrected by _David A. Corneth_, Apr 23 2016

%E a(16) from _Michael S. Branicky_, May 29 2024

%E a(17) from _Michael S. Branicky_, Jun 26 2024

%E a(18) from _Michael S. Branicky_, Jul 08 2024