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%I #46 Sep 26 2019 04:18:43
%S 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 72,78,80,84,88,90,94,96,98,102,108,114,118,120,122,124,126,128,138,
%U 146,148,150,158,164,174,180,188,190,192,206,208,210,212,218,220,222,224
%N Even integers k such that there exists a prime p with p = min{q: q prime and (k - q) prime} and (k - p) < p^3.
%C It is conjectured that the sequence is finite with last term a(104820) = 5714500178 and it is proven that there are no more terms below 4*10^18. This is an extension of A307542. - _Corinna Regina Böger_, Apr 14 2019
%H Corinna Regina Böger, <a href="/A093161/b093161.txt">Table of n, a(n) for n = 1..10000</a>
%H Corinna Regina Böger, <a href="/A093161/a093161.txt">a-file, Table of n, a(n) for n=1..104820</a>
%H John F. Nash, Jr., <a href="https://web.archive.org/web/20090130033705/http://www.math.princeton.edu/jfnj/texts_and_graphics/Goldbach_Programs/">Goldbach Programs</a>
%e 63274 is in the sequence because 63274 = 293 + 62981 is the Goldbach partition with the smallest prime and 293^3 = 25153757 is > 62981. [clarified by _Corinna Regina Böger_, Apr 22 2019]
%p isS := proc(n) local p; for p from 2 while p^3 < (n-p) do
%p if isprime(p) and isprime(n-p) then return false fi od; true end:
%p isa := n -> irem(n,2) = 0 and isS(n): select(isa, [$4..224]); # _Peter Luschny_, Apr 26 2019
%t okQ[n_] := Module[{p}, For[p = 2, p <= n/2, p = NextPrime[p], If[p^3 + p < n && PrimeQ[n - p], Return[False]]]; True];
%t Select[Range[4, 250, 2], okQ] (* _Jean-François Alcover_, Jun 11 2019, from PARI *)
%o (PARI) noSpecialGoldbach(n) = forprime(p=2, n/2, if(p^3+p<n && isprime(n-p), return(0))); 1
%o is(n) = n>2 && n%2 == 0 && noSpecialGoldbach(n) \\ _Corinna Regina Böger_, Apr 14 2019
%Y Cf. A025018.
%K easy,nonn
%O 1,1
%A _Jason Earls_, May 10 2004
%E New name by _Corinna Regina Böger_, Apr 27 2019
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