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 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; then a(n) = max_u f(u). 10
 1, 2, 4, 8, 21, 60, 269, 1147, 4250, 17883, 71966, 342060, 1724337, 8428101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS EXAMPLE a(2)=2 because 15 and 51 (written in base 6) are primes (11 and 31). MAPLE A065847 := proc(n)     local b, u, udgs, uperm, a;     b :=6 ;     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, A065847(n)) ; end do: # R. J. Mathar, Apr 23 2016 MATHEMATICA c[x_] := Module[{},    Length[Select[Permutations[x],      First[#] != 0 && PrimeQ[FromDigits[#, 6]] &]]]; A065847[n_] := Module[{i},    Return[Max[Map[c, DeleteDuplicatesBy[Tuples[Range[0, 5], n],        Table[Count[#, i], {i, 0, 5}] &]]]]]; Table[A065847[n], {n, 1, 8}] (* Robert Price, Mar 30 2019 *) PROG (Python) from sympy import isprime from sympy.utilities.iterables import multiset_permutations from itertools import combinations_with_replacement def A065847(n):     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 CROSSREFS Cf. A065843, A065844, A065845, A065846, A065848, A065849, A065850, A065851, A065852, A065853 Sequence in context: A162110 A108071 A055876 * A133604 A262345 A192149 Adjacent sequences:  A065844 A065845 A065846 * A065848 A065849 A065850 KEYWORD base,more,nonn AUTHOR Sascha Kurz, Nov 24 2001 EXTENSIONS a(12)-a(13) from Sean A. Irvine, Sep 06 2009 Definition corrected by David A. Corneth, Apr 23 2016 a(14) from Chai Wah Wu, Jun 15 2019 STATUS approved

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Last modified January 24 13:24 EST 2020. Contains 331193 sequences. (Running on oeis4.)