A307782 -id:A307782 - 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).

4, 6, 8, 12, 18, 24, 30, 38, 98, 122, 126, 128, 220, 302, 308, 332, 346, 488, 556, 854, 908, 962, 992, 1144, 1150, 1274, 1354, 1360, 1362, 1382, 1408, 1424, 1532, 1768, 1856, 1928, 2078, 2188, 2200, 2438, 2512, 2530, 2618, 2642, 3458, 3818, 3848

Offset: 1

Jon Perry, Jun 27 2014

nonn

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

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

			The smallest prime for 38 is 7, and 7 >= sqrt(38).

Jens Kruse Andersen, Table of n, a(n) for n = 1..74
Tomás Oliveira e Silva, Goldbach conjecture verification
Index entries for sequences related to Goldbach conjecture

Cf. A020481, A002373, A025018, A025019, A306746, A307782.

a244408 n = a244408_list !! (n-1)
a244408_list = map (* 2) $ filter f [2..] where
   f x = sqrt (fromIntegral $ 2 * x) <= fromIntegral (a020481 x)
-- Reinhard Zumkeller, Jul 07 2014

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

A279040 Even numbers 2k such that the smallest prime p satisfying p+q=2k (q prime) is greater than or equal to sqrt(k).

Original entry on oeis.org

4, 6, 8, 10, 12, 14, 16, 18, 24, 28, 30, 36, 38, 42, 48, 54, 60, 68, 80, 90, 96, 98, 122, 124, 126, 128, 148, 150, 190, 192, 208, 210, 212, 220, 222, 224, 302, 306, 308, 326, 330, 332, 346, 368, 398, 418, 458, 488, 518, 538, 540, 542, 556, 640, 692, 710, 796, 854, 908, 962, 968, 992, 1006

Offset: 1

Corinna Regina Böger, Dec 04 2016

nonn

a(n) is an extension of A244408.
It is conjectured that a(230) = 503222 is the last term. Oliveira e Silva's work shows that there are no more terms below 4*10^18.
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 < 2*p^2" and therefore this is a member of the EGN- family (Cf. A307782). - Corinna Regina Böger, May 01 2019

			The smallest prime for 42 is 5 with 5 > sqrt(21), but not smaller than sqrt(42), and therefore 42 does not belong to A244408. The smallest prime for 38 is 7, and 7 >= sqrt(38), and therefore 38 also belongs to A244408.

Corinna Regina Böger, Table of n, a(n) for n = 1..230
Tomás Oliveira e Silva, Goldbach conjecture verification
Index entries for sequences related to Goldbach conjecture

Cf. A002373, A020481, A025018, A025019, A093161, A244408, A307542, A307782

Select[Range[4, 1006, 2], Function[n, Select[#, PrimeQ@ Last@ # &][[1, 1]] >= Sqrt[n/2] &@ Map[{#, n - #} &, Prime@ Range@ PrimePi@ n]]] (* Michael De Vlieger, Dec 06 2016 *)

isok(n) = forprime(p=2, n, if (isprime(n-p), if (p >= sqrt(n/2), return(1), return(0))));
lista(nn) = forstep(n=2, nn, 2, if (isok(n), print1(n, ", "))) \\ Michel Marcus, Dec 04 2016

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).

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