cp's OEIS Frontend

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).

%I A065847 #37 Jul 02 2024 14:50:39
%S A065847 1,2,4,8,21,60,269,1147,4250,17883,71966,342060,1724337,8428101,
%T A065847 37186164,175845403
%N 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).
%e A065847 a(2)=2 because 15 and 51 (written in base 6) are primes (11 and 31).
%p A065847 A065847 := proc(n)
%p A065847     local b,u,udgs,uperm,a;
%p A065847     b :=6 ;
%p A065847     a := 0 ;
%p A065847     for u from b^(n-1) to b^n-1 do
%p A065847         udgs := convert(u,base,b) ;
%p A065847         prs := {} ;
%p A065847         for uperm in combinat[permute](udgs) do
%p A065847             if op(-1,uperm) <> 0 then
%p A065847                 p := add( op(i,uperm)*b^(i-1),i=1..nops(uperm)) ;
%p A065847                 if isprime(p) then
%p A065847                     prs := prs union {p} ;
%p A065847                 end if;
%p A065847             end if;
%p A065847         end do:
%p A065847         a := max(a,nops(prs)) ;
%p A065847     end do:
%p A065847     a ;
%p A065847 end proc:
%p A065847 for n from 1 do
%p A065847     print(n,A065847(n)) ;
%p A065847 end do: # _R. J. Mathar_, Apr 23 2016
%t A065847 c[x_] := Module[{},
%t A065847    Length[Select[Permutations[x],
%t A065847      First[#] != 0 && PrimeQ[FromDigits[#, 6]] &]]];
%t A065847 A065847[n_] := Module[{i},
%t A065847    Return[Max[Map[c, DeleteDuplicatesBy[Tuples[Range[0, 5], n],
%t A065847        Table[Count[#, i], {i, 0, 5}] &]]]]];
%t A065847 Table[A065847[n], {n, 1, 8}] (* _Robert Price_, Mar 30 2019 *)
%o A065847 (Python)
%o A065847 from sympy import isprime
%o A065847 from sympy.utilities.iterables import multiset_permutations
%o A065847 from itertools import combinations_with_replacement
%o A065847 def A065847(n):
%o A065847     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
%Y A065847 Cf. A065843, A065844, A065845, A065846, A065848, A065849, A065850, A065851, A065852, A065853.
%K A065847 base,more,nonn
%O A065847 1,2
%A A065847 _Sascha Kurz_, Nov 24 2001
%E A065847 a(12)-a(13) from _Sean A. Irvine_, Sep 06 2009
%E A065847 Definition corrected by _David A. Corneth_, Apr 23 2016
%E A065847 a(14) from _Chai Wah Wu_, Jun 15 2019
%E A065847 a(15) from _Michael S. Branicky_, Jun 25 2024
%E A065847 a(16) from _Michael S. Branicky_, Jul 02 2024