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

2, 4, 6, 32, 56, 92, 98, 122, 128, 140, 152, 176, 194, 212, 224, 242, 254, 260, 272, 296, 302, 308, 326, 332, 368, 392, 398, 410, 422, 434, 452, 458, 476, 488, 500, 512, 518, 524, 536, 542, 560, 572, 596, 602, 632, 644, 656, 662, 674, 686, 692, 704, 710, 728

Offset

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

StackExchange, Even numbers greater than 6 as sum of two specific primes

Mathematica

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 *)

Prog

#!/usr/bin/perl
$| = 1;
sub is_prime {
  my $n = shift;
  return 0 if $n < 2;
  return 1 if $n == 2;
  return 0 unless $n % 2;
  my $sn = int(sqrt($n));
  for (my $j = 3; $j <= $sn; $j += 2) {
    return 0 if $n % $j == 0;
  }
  return 1;
}
my $n = 0;
while (1) {
  ++$n;
  next if $n % 2;
  my $found = 0;
  for my $p (3 .. $n) {
    next unless $p % 2;
    my $q = $n - $p;
    next unless $q % 2;
    next unless is_prime($p);
    next unless is_prime($q);
    next unless is_prime(($p - 1) / 2) || is_prime(($q - 1) / 2);
    $found = 1;
    last;
  }
  print "$n\n" unless $found;
}
(Haskell)
a195324 n = a195324_list !! (n-1)
a195324_list = filter p [2, 4..] where
   p n = all ((== 0) . a010051) $ takeWhile (> 1) $ map (n -) a005385_list
-- Reinhard Zumkeller, Sep 18 2011

Crossrefs

Cf. A000040 (primes), A005385 (safe primes).

Sequence in context: A100838 A056696 A045662 * A175877 A269265 A173818

Adjacent sequences: A195321 A195322 A195323 * A195325 A195326 A195327

Keyword

nonn

Author

Dan Brumleve, Sep 15 2011

Status

approved