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A163555
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Composite numbers such that exactly three distinct permutations of digits give primes.
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3
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130, 136, 175, 176, 301, 310, 316, 361, 370, 371, 395, 398, 517, 539, 671, 703, 713, 715, 716, 730, 731, 893, 935, 938, 1004, 1025, 1027, 1034, 1040, 1043, 1052, 1058, 1072, 1085, 1118, 1124, 1142, 1147, 1169, 1174, 1189, 1196, 1198, 1205, 1207, 1214
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(1) = 130 because 130 is composite and 13, 31, and 103 are prime permutations, and no other permutation of 130 is prime.
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MAPLE
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filter:= proc(n) local d, Permutor, P, c, i;
if isprime(n) then return false fi;
d:= ilog10(n)+1;
Permutor:= Iterator:-Permute(convert(n, base, 10));
c:= 0;
for P in Permutor do
if isprime(add(P[i]*10^(i-1), i=1..d)) then
c:= c+1;
if c >= 4 then return false fi;
fi
od;
evalb(c=3)
end proc:
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MATHEMATICA
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With[{no=1400}, Select[Complement[Range[no], Prime[Range[PrimePi[no]]]], Count[FromDigits/@Permutations[IntegerDigits[#]], _?PrimeQ]==3&]] (* Harvey P. Dale, Feb 25 2011 *)
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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STATUS
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approved
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