OFFSET
1,1
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
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
EXAMPLE
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]
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 *)
PROG
(PARI) noSpecialGoldbach(n) = forprime(p=2, n/2, if(p^3+p<n && isprime(n-p), return(0))); 1
is(n) = n>2 && n%2 == 0 && noSpecialGoldbach(n) \\ Corinna Regina Böger, Apr 14 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jason Earls, May 10 2004
EXTENSIONS
New name by Corinna Regina Böger, Apr 27 2019
STATUS
approved