A244408 - OEIS

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

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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 (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

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*n-p), if(p>=sqrt(2*n), print1(2*n", ")); break))) \\ Jens Kruse Andersen, Jul 03 2014

(Haskell)

a244408 n = a244408_list !! (n-1)

a244408_list = map (* 2) $ filter f [2..] where

f x = sqrt (fromIntegral $ 2 * x) <= fromIntegral (a020481 x)