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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).

%I A065845 #31 Jun 23 2024 11:51:16
%S A065845 1,2,3,6,13,36,96,253,765,2683,7385,25075,83150,293063,888689,3161645,
%T A065845 11097301,40328876,129951350,469528189,1694632516
%N 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).
%e A065845 a(2)=2 because 13 and 31 (written in base 4) are primes (7 and 13).
%p A065845 A065845 := proc(n)
%p A065845     local b,u,udgs,uperm,a;
%p A065845     b :=4 ;
%p A065845     a := 0 ;
%p A065845     for u from b^(n-1) to b^n-1 do
%p A065845         udgs := convert(u,base,b) ;
%p A065845         prs := {} ;
%p A065845         for uperm in combinat[permute](udgs) do
%p A065845             if op(-1,uperm) <> 0 then
%p A065845                 p := add( op(i,uperm)*b^(i-1),i=1..nops(uperm)) ;
%p A065845                 if isprime(p) then
%p A065845                     prs := prs union {p} ;
%p A065845                 end if;
%p A065845             end if;
%p A065845         end do:
%p A065845         a := max(a,nops(prs)) ;
%p A065845     end do:
%p A065845     a ;
%p A065845 end proc:
%p A065845 for n from 1 do
%p A065845     print(n,A065845(n)) ;
%p A065845 end do: # _R. J. Mathar_, Apr 23 2016
%t A065845 c[x_] := Module[{},
%t A065845    Length[Select[Permutations[x],
%t A065845      First[#] != 0 && PrimeQ[FromDigits[#, 4]] &]]];
%t A065845 A065845[n_] := Module[{i},
%t A065845    Return[Max[Map[c, DeleteDuplicatesBy[Tuples[Range[0, 3], n],
%t A065845        Table[Count[#, i], {i, 0, 3}] &]]]]];
%t A065845 Table[A065845[n], {n, 1, 10}] (* _Robert Price_, Mar 30 2019 *)
%Y A065845 Cf. A065843, A065844, A065846, A065847, A065848, A065849, A065850, A065851, A065852, A065853
%K A065845 base,more,nonn
%O A065845 1,2
%A A065845 _Sascha Kurz_, Nov 24 2001
%E A065845 3 more terms from _Sean A. Irvine_, Sep 06 2009
%E A065845 Definition corrected by _David A. Corneth_, Apr 23 2016
%E A065845 a(19) from _Michael S. Branicky_, May 29 2024
%E A065845 a(20)-a(21) from _Michael S. Branicky_, Jun 14 2024