

A244408


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


8



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
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OFFSET

1,1


COMMENTS

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 (kq) prime} and k <= p^2" and therefore this is a member of the EGNfamily (Cf. A307782).  Corinna Regina Böger, May 01 2019


LINKS

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


EXAMPLE

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


PROG

(PARI) for(n=1, 50000, forprime(p=2, n, if(isprime(2*np), if(p>=sqrt(2*n), print1(2*n", ")); break))) \\ Jens Kruse Andersen, Jul 03 2014
(Haskell)
a244408 n = a244408_list !! (n1)
a244408_list = map (* 2) $ filter f [2..] where
f x = sqrt (fromIntegral $ 2 * x) <= fromIntegral (a020481 x)
 Reinhard Zumkeller, Jul 07 2014


CROSSREFS

Cf. A020481, A002373, A025018, A025019, A306746, A307782.
Sequence in context: A161785 A234523 A178549 * A023374 A053016 A078785
Adjacent sequences: A244405 A244406 A244407 * A244409 A244410 A244411


KEYWORD

nonn


AUTHOR

Jon Perry, Jun 27 2014


STATUS

approved



