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