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A279040 Even numbers 2k such that the smallest prime p satisfying p+q=2k (q prime) is greater than or equal to sqrt(k). 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
Corinna Regina Böger, Table of n, a(n) for n = 1..230
Tomás Oliveira e Silva, Goldbach conjecture verification
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(PARI) 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
CROSSREFS
Sequence in context: A175246 A353537 A134928 * A141109 A333197 A289426
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified May 29 21:02 EDT 2024. Contains 372952 sequences. (Running on oeis4.)