OFFSET
1,1
COMMENTS
A subsequence of A254671.
From Robert Israel, May 27 2015: (Start)
n such that n+1 is not prime and not twice a prime, but every divisor of n+1 except for 1, 2, n+1 and (n+1)/2 is in A008864.
a(7) > 10^7 if it exists. (End)
EXAMPLE
23 = 5*3 + 5 + 3 = 7*2 + 7 + 2, and 2,3,5,7 are all primes, so 23 is a term.
71 = 11*5 + 11 + 5 = 17*3 + 17 + 3 = 23*2 + 23 + 2 = 7*8 + 8 + 7, but 8 is not a prime so 71 is not a term.
35 = 5*5 + 5 + 5 = 11*2 + 11 + 2 = 8*3 + 8 + 3, but 8 is not a prime so 35 is not a term.
MAPLE
filter:= proc(n)
local D;
D:= map(`-`, numtheory:-divisors(n+1) minus {1, 2, n+1, (n+1)/2}, 1);
nops(D) >= 1 and andmap(isprime, D);
end proc:
select(filter, [$1..10^6]); # Robert Israel, May 27 2015
MATHEMATICA
sol[t_] := Solve[x >= y > 1 && x y + x + y == t, {x, y}, Integers];
Select[Range[100], AllTrue[Flatten[{x, y} /. sol[#]], PrimeQ]&] (* Jean-François Alcover, Jul 28 2020 *)
PROG
(Python)
import sympy
from sympy import isprime
TOP = 10000
a = [0]*TOP
no= [0]*TOP
for y in range(2, TOP//2):
for x in range(y, TOP//2):
k = x*y + x + y
if k>=TOP: break
if no[k]==0:
a[k]=1
if not (isprime(x) and isprime(y)): no[k]=1
print([n for n in range(TOP) if a[n]>0 and no[n]==0])
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Mar 14 2015
EXTENSIONS
More terms from Lars Blomberg, May 01 2015
Incorrect terms removed by Alex Ratushnyak, May 27 2015
STATUS
approved