A093161 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.

4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 36, 38, 42, 48, 52, 54, 58, 60, 66, 68, 72, 78, 80, 84, 88, 90, 94, 96, 98, 102, 108, 114, 118, 120, 122, 124, 126, 128, 138, 146, 148, 150, 158, 164, 174, 180, 188, 190, 192, 206, 208, 210, 212, 218, 220, 222, 224

Offset: 1

Author

Jason Earls, May 10 2004

Keywords

• easy
• nonn

Comments

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

Examples

			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]
		

Links

• Corinna Regina Böger, Table of n, a(n) for n = 1..10000
• Corinna Regina Böger, a-file, Table of n, a(n) for n=1..104820
• John F. Nash, Jr., Goldbach Programs

Crossrefs

Cf. A025018.

Programs

Maple

isS := proc(n) local p; for p from 2 while p^3 < (n-p) do
if isprime(p) and isprime(n-p) then return false fi od; true end:
isa := n -> irem(n,2) = 0 and isS(n): select(isa, [$4..224]); # Peter Luschny, Apr 26 2019

Mathematica

okQ[n_] := Module[{p}, For[p = 2, p <= n/2, p = NextPrime[p], If[p^3 + p < n && PrimeQ[n - p], Return[False]]]; True];
Select[Range[4, 250, 2], okQ] (* Jean-François Alcover, Jun 11 2019, from PARI *)

PARI

noSpecialGoldbach(n) = forprime(p=2, n/2, if(p^3+p2 && n%2 == 0 && noSpecialGoldbach(n) \\ Corinna Regina Böger, Apr 14 2019

Extensions

New name by Corinna Regina Böger, Apr 27 2019