cp's OEIS Frontend

A307782 Even integers k such that there exists a prime p with p=min{q: q prime and (k-q) prime} and k < p^3.

%I A307782 #18 Sep 01 2019 22:01:53
%S A307782 4,6,8,10,12,14,16,18,20,22,24,26,28,30,36,38,42,48,52,54,58,60,66,68,
%T A307782 72,78,80,84,88,90,94,96,98,102,108,114,118,120,122,124,126,128,138,
%U A307782 146,148,150,158,164,174,180,188,190,192,206,208,210,212,218,220,222,224,240,248,250,252,258,264,270,278,290,292,294,300,302,304,306,308,324,326,328,330,332,338,346
%N A307782 Even integers k such that there exists a prime p with p=min{q: q prime and (k-q) prime} and k < p^3.
%C A307782 [Please keep the larger data section as it shows where the sequence first differs from A093161.]
%C A307782 This is another member of a family of sequences concerning the Strong Goldbach Conjecture, which I define as follows: Let (x, y, z) be real numbers with x >= 2, y > 0, z >= 0. An even integer k is then called an (x, y, z) Extraordinary Goldbach Number (EGN) if there exists a prime p with p=min{q: q prime and (k-q) prime} and (k - z*p) < y*p^x. a(n) represents the (3, 1, 0) extraordinary Goldbach numbers. A093161 consists of (3, 1, 1) EGN, A307542 are the (2, 1, 1) EGN, A279040 are the (2, 2, 0) EGN and A244408 are the (2, 1, 0).
%C A307782 a(104809) is very probably the last term and there are no more terms below 4*10^18.
%C A307782 There are only 11 terms in A093161 that are not in this sequence; these are 344, 1338, 12184, 12186, 24400, 148912, 1030342, 2571406, 3308008, 5929868, 15813352.
%H A307782 Corinna Regina Böger, <a href="/A307782/b307782.txt">Table of n, a(n) for n = 1..10000</a>
%H A307782 Corinna Regina Böger, <a href="/A307782/a307782.txt">a-file, Table of n, a(n) for n = 1..104809</a>
%e A307782 344 is not in the sequence, because the smallest prime p for 344 is 7 with 7^3 = 343 < 344, whereas it is in A093161 due to 344 - 7 = 337 < 7^3.
%o A307782 (PARI) extraordinaryGoldbach(x,y,z,k) = forprime(p=2, k/2, if(isprime(k-p), if(y*p^x+z*p>=k, return(1),return(0)))); 0
%o A307782 is(n) = n%2 == 0 && extraordinaryGoldbach(3, 1, 0, n)
%Y A307782 Cf. A093161, A244408, A279040, A307542.
%K A307782 nonn
%O A307782 1,1
%A A307782 _Corinna Regina Böger_, Apr 28 2019