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 A065843 Let u be any string of n digits from {0,1}; 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). 11
 0, 1, 1, 2, 2, 3, 5, 12, 11, 24, 34, 79, 105, 194, 362, 734, 1143, 2045, 3872, 7758, 13001, 23902, 45539, 90436, 159510, 296210, 563833, 1110387, 2030754, 3876871, 7333827, 14353074, 26730538, 51246344, 97529176, 190928828 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS EXAMPLE a(4)=2 because 1011 and 1101 in base-2 notation are primes (11 and 13) and there is no set of three or more 4-digit primes with a common number of ones. MAPLE A065843 := proc(n)     local b, u, udgs, uperm, a;     b :=2 ;     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, A065843(n)) ; end do: # R. J. Mathar, Apr 23 2016 MATHEMATICA c[x_] := Module[{},    Length[Select[Permutations[x],      First[#] != 0 && PrimeQ[FromDigits[#, 2]] &]]]; A065843[n_] := Module[{i},    Return[Max[Map[c, DeleteDuplicatesBy[Tuples[Range[0, 1], n],        Table[Count[#, i], {i, 0, 1}] &]]]]]; Table[A065843[n], {n, 1, 19}] (* Robert Price, Mar 30 2019 *) PROG (PARI) lista(n) = {my(m = matrix(n, n), c); forprime(i=2, 2^n, b = binary(i); m[#b, hammingweight(b)]++); vector(n, i, vecmax(m[i, ]))} \\ David A. Corneth, Apr 23 2016 CROSSREFS Cf. A065844 - A065853 Sequence in context: A005426 A014644 A089541 * A111264 A065994 A152446 Adjacent sequences:  A065840 A065841 A065842 * A065844 A065845 A065846 KEYWORD base,nonn AUTHOR Sascha Kurz, Nov 24 2001 EXTENSIONS 6 more terms from Sean A. Irvine, Sep 06 2009 STATUS approved

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Last modified July 26 01:20 EDT 2021. Contains 346294 sequences. (Running on oeis4.)