OFFSET
1,1
COMMENTS
Dickson's conjecture implies that for every prime p that does not divide 2*n-1, there exist infinitely many q such that q and 2*p*q-(2*n-1) are prime. Thus a(n) always exists.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Mathematics StackExchange, Can every odd number be represented as 2pq-r where p, q, and r are distinct odd primes?
EXAMPLE
a(3)=13 because 2*3-1+13 = 18 = 2*3*3 with 13, 3, 3 all primes, and 13 is the least prime for which this works.
MAPLE
f:= proc(m) local r, x;
r:= 2:
do r:= nextprime(r);
x:= (m+r)/2;
if x::odd and numtheory:-bigomega(x)=2 then return r
fi od
end proc:
map(f, [seq(i, i=1..1000, 2)]);
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Nov 25 2019
STATUS
approved