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A195324 Even numbers that cannot be represented as the sum of an odd prime and a safe prime (A005385). 1
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 (list; graph; refs; listen; history; text; internal format)
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 A173818 A084324

Adjacent sequences:  A195321 A195322 A195323 * A195325 A195326 A195327

KEYWORD

nonn

AUTHOR

Dan Brumleve, Sep 15 2011

STATUS

approved

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Last modified April 25 03:36 EDT 2014. Contains 240994 sequences.