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%I #14 Aug 10 2020 13:18:08
%S 130,136,175,176,301,310,316,361,370,371,395,398,517,539,671,703,713,
%T 715,716,730,731,893,935,938,1004,1025,1027,1034,1040,1043,1052,1058,
%U 1072,1085,1118,1124,1142,1147,1169,1174,1189,1196,1198,1205,1207,1214
%N Composite numbers such that exactly three distinct permutations of digits give primes.
%H Robert Israel, <a href="/A163555/b163555.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 130 because 130 is composite and 13, 31, and 103 are prime permutations, and no other permutation of 130 is prime.
%p filter:= proc(n) local d, Permutor, P, c, i;
%p if isprime(n) then return false fi;
%p d:= ilog10(n)+1;
%p Permutor:= Iterator:-Permute(convert(n, base, 10));
%p c:= 0;
%p for P in Permutor do
%p if isprime(add(P[i]*10^(i-1), i=1..d)) then
%p c:= c+1;
%p if c >= 4 then return false fi;
%p fi
%p od;
%p evalb(c=3)
%p end proc:
%p select(filter, [$100..2000]); # _Robert Israel_, Aug 10 2020
%t With[{no=1400},Select[Complement[Range[no],Prime[Range[PrimePi[no]]]],Count[FromDigits/@Permutations[IntegerDigits[#]],_?PrimeQ]==3&]] (* _Harvey P. Dale_, Feb 25 2011 *)
%Y Cf. A163554, A163556, A163557, A163558, A163559, A163560, A163561, A163562.
%K easy,nonn,base
%O 1,1
%A _Gil Broussard_, Jul 30 2009
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