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A065844
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Let u be any string of n digits from {0,1,2}; let f(u) = number of distinct primes, not beginning with 0, formed by permuting the digits of u to a base-3 number; then a(n) = max_u f(u).
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11
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1, 2, 2, 4, 7, 19, 42, 102, 252, 532, 1226, 3681, 9100, 24858, 61943, 161857, 392935, 1167208, 3125539, 8879693, 23143081, 63028550, 161146767, 480399716, 1325189141, 3815350317, 10255072974
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OFFSET
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1,2
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COMMENTS
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a(25) >= 1325189141 via permutations of numbers with eight 0's, nine 1's and eight 2's. If some permutation class gives a larger number of primes then it's smallest element is lexicographically larger than 1000000001111111111111222. Permutation class 1000000011111111222222222 gives fewer primes than 1325189141. - David A. Corneth, May 31 2024
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LINKS
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EXAMPLE
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a(2)=2 because 12 and 21 (written in base 3) are primes (5 and 7).
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MAPLE
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local b, u, udgs, uperm, a;
b :=3 ;
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
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MATHEMATICA
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c[x_] := Module[{},
Length[Select[Permutations[x],
First[#] != 0 && PrimeQ[FromDigits[#, 3]] &]]];
Return[Max[Map[c, DeleteDuplicatesBy[Tuples[Range[0, 2], n],
Table[Count[#, i], {i, 0, 2}] &]]]]];
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CROSSREFS
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Cf. A055729, A065843, A065845, A065846, A065847, A065848, A065849, A065850, A065851, A065852, A065853
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KEYWORD
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base,nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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