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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; then a(n) = max_u f(u). 10
1, 2, 3, 6, 13, 36, 96, 253, 765, 2683, 7385, 25075, 83150, 293063, 888689, 3161645, 11097301, 40328876 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..18.

EXAMPLE

a(2)=2 because 13 and 31 (written in base 4) are primes (7 and 13).

MAPLE

A065845 := proc(n)

    local b, u, udgs, uperm, a;

    b :=4 ;

    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, A065845(n)) ;

end do: # R. J. Mathar, Apr 23 2016

MATHEMATICA

c[x_] := Module[{},

   Length[Select[Permutations[x],

     First[#] != 0 && PrimeQ[FromDigits[#, 4]] &]]];

A065845[n_] := Module[{i},

   Return[Max[Map[c, DeleteDuplicatesBy[Tuples[Range[0, 3], n],

       Table[Count[#, i], {i, 0, 3}] &]]]]];

Table[A065845[n], {n, 1, 10}] (* Robert Price, Mar 30 2019 *)

CROSSREFS

Cf. A065843, A065844, A065846, A065847, A065848, A065849, A065850, A065851, A065852, A065853

Sequence in context: A171878 A117403 A002877 * A137273 A135967 A290248

Adjacent sequences:  A065842 A065843 A065844 * A065846 A065847 A065848

KEYWORD

base,more,nonn

AUTHOR

Sascha Kurz, Nov 24 2001

EXTENSIONS

3 more terms from Sean A. Irvine, Sep 06 2009

Definition corrected by David A. Corneth, Apr 23 2016

STATUS

approved

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Last modified January 28 06:29 EST 2020. Contains 331317 sequences. (Running on oeis4.)