OFFSET
1,1
COMMENTS
This sequence is an extension of A244408. It is equivalent to "Even numbers 2n such that the smallest prime p satisfying p+q=2n (p, q prime, p<=q) also satisfies p^2+p>2n." If p satisfies additionally p^2 < 2n the corresponding even numbers do not belong to A244408. These numbers are 10, 28, 54, 124, 368, 968, 3526. It is conjectured that a(81)=63274 is the last term. There are no more terms below 4*10^18.
LINKS
Corinna Regina Böger, Table of n, a(n) for n = 1..81
EXAMPLE
10 = 3 + 7, 3^2 = 9 < 10 and 9 > 7 = q, therefore it is in this sequence.
MAPLE
isS := proc(n) local p; for p from 2 while p^2 < (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..3848]); # Peter Luschny, Apr 26 2019
MATHEMATICA
Select[Range[4, 4000, 2], #2 > Sqrt@ #1 & @@ SelectFirst[IntegerPartitions[#, {2}], AllTrue[#, PrimeQ] &] &] (* Michael De Vlieger, Apr 21 2019 *)
PROG
(PARI) noSpecialGoldbach(n) = forprime(p=2, n/2, if(p^2+p<n && isprime(n-p), return(0))); 1
is(n) = n>2 && n%2 == 0 && noSpecialGoldbach(n)
CROSSREFS
KEYWORD
nonn
AUTHOR
Corinna Regina Böger, Apr 14 2019
STATUS
approved