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A195324 Even numbers that cannot be represented as the sum of an odd prime and a safe prime (A005385).

%I A195324 #15 Aug 03 2014 14:01:33
%S A195324 2,4,6,32,56,92,98,122,128,140,152,176,194,212,224,242,254,260,272,
%T A195324 296,302,308,326,332,368,392,398,410,422,434,452,458,476,488,500,512,
%U A195324 518,524,536,542,560,572,596,602,632,644,656,662,674,686,692,704,710,728
%N A195324 Even numbers that cannot be represented as the sum of an odd prime and a safe prime (A005385).
%H A195324 Reinhard Zumkeller, <a href="/A195324/b195324.txt">Table of n, a(n) for n = 1..10000</a>
%H A195324 StackExchange, <a href="http://math.stackexchange.com/questions/64109/even-numbers-greater-than-6-as-sum-of-two-specific-primes/64111#64111">Even numbers greater than 6 as sum of two specific primes</a>
%t A195324 mx = 1000; safe = Select[Prime[Range[PrimePi[mx]]], PrimeQ[(# - 1)/2] &]; p = Prime[Range[2, PrimePi[mx]]]; Complement[Range[2, mx, 2], Union[Flatten[Outer[Plus, p, t]]]] (* _T. D. Noe_, Sep 15 2011 *)
%o A195324 #!/usr/bin/perl
%o A195324 $| = 1;
%o A195324 sub is_prime {
%o A195324   my $n = shift;
%o A195324   return 0 if $n < 2;
%o A195324   return 1 if $n == 2;
%o A195324   return 0 unless $n % 2;
%o A195324   my $sn = int(sqrt($n));
%o A195324   for (my $j = 3; $j <= $sn; $j += 2) {
%o A195324     return 0 if $n % $j == 0;
%o A195324   }
%o A195324   return 1;
%o A195324 }
%o A195324 my $n = 0;
%o A195324 while (1) {
%o A195324   ++$n;
%o A195324   next if $n % 2;
%o A195324   my $found = 0;
%o A195324   for my $p (3 .. $n) {
%o A195324     next unless $p % 2;
%o A195324     my $q = $n - $p;
%o A195324     next unless $q % 2;
%o A195324     next unless is_prime($p);
%o A195324     next unless is_prime($q);
%o A195324     next unless is_prime(($p - 1) / 2) || is_prime(($q - 1) / 2);
%o A195324     $found = 1;
%o A195324     last;
%o A195324   }
%o A195324   print "$n\n" unless $found;
%o A195324 }
%o A195324 (Haskell)
%o A195324 a195324 n = a195324_list !! (n-1)
%o A195324 a195324_list = filter p [2,4..] where
%o A195324    p n = all ((== 0) . a010051) $ takeWhile (> 1) $ map (n -) a005385_list
%o A195324 -- _Reinhard Zumkeller_, Sep 18 2011
%Y A195324 Cf. A000040 (primes), A005385 (safe primes).
%K A195324 nonn
%O A195324 1,1
%A A195324 _Dan Brumleve_, Sep 15 2011