cp's OEIS Frontend

A244408 Even numbers 2k such that the smallest prime p satisfying p+q=2k (q prime) is greater than or equal to sqrt(2k).

%I A244408 #41 May 01 2019 09:13:03
%S A244408 4,6,8,12,18,24,30,38,98,122,126,128,220,302,308,332,346,488,556,854,
%T A244408 908,962,992,1144,1150,1274,1354,1360,1362,1382,1408,1424,1532,1768,
%U A244408 1856,1928,2078,2188,2200,2438,2512,2530,2618,2642,3458,3818,3848
%N A244408 Even numbers 2k such that the smallest prime p satisfying p+q=2k (q prime) is greater than or equal to sqrt(2k).
%C A244408 a(74) = 63274 is probably the last term. Oliveira e Silva's work shows there are no more terms below 4*10^18. The largest p below that is p = 9781 for 2k = 3325581707333960528, where sqrt(2k) = 1823617752. - _Jens Kruse Andersen_, Jul 03 2014
%C A244408 The sequence definition is equivalent to: "Even integers k such that there exists a prime p with p = min{q: q prime and (k-q) prime} and k <= p^2" and therefore this is a member of the EGN-family (Cf. A307782). - _Corinna Regina Böger_, May 01 2019
%H A244408 Jens Kruse Andersen, <a href="/A244408/b244408.txt">Table of n, a(n) for n = 1..74</a>
%H A244408 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/goldbach.html">Goldbach conjecture verification</a>
%H A244408 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%e A244408 The smallest prime for 38 is 7, and 7 >= sqrt(38).
%o A244408 (PARI) for(n=1, 50000, forprime(p=2, n, if(isprime(2*n-p), if(p>=sqrt(2*n), print1(2*n", ")); break))) \\ _Jens Kruse Andersen_, Jul 03 2014
%o A244408 (Haskell)
%o A244408 a244408 n = a244408_list !! (n-1)
%o A244408 a244408_list = map (* 2) $ filter f [2..] where
%o A244408    f x = sqrt (fromIntegral $ 2 * x) <= fromIntegral (a020481 x)
%o A244408 -- _Reinhard Zumkeller_, Jul 07 2014
%Y A244408 Cf. A020481, A002373, A025018, A025019, A306746, A307782.
%K A244408 nonn
%O A244408 1,1
%A A244408 _Jon Perry_, Jun 27 2014