login
A356108
Numbers == 2 (mod 6) that cannot be written as p^2 + q where p and q are primes.
1
2, 8, 74, 170, 614, 704, 1010, 24476
OFFSET
1,1
COMMENTS
Numbers k == 2 (mod 6) such that A356077(k/2) = -1.
a(9) > 10^7 if it exists.
There are many numbers == 0 (mod 6) that cannot be written as p^2 + q, but nearly all of them are squares.
EXAMPLE
a(3) = 74 is a term because 74 == 2 (mod 6) and none of 74 - 2^2 = 70, 74 - 3^2 = 65, 74 - 5^2 = 49, 74 - 7^2 = 25 are prime.
MAPLE
filter:= proc(n) local p;
p:= 2;
do
p:= nextprime(p);
if n <= p^2 then return true fi;
if isprime(n-p^2) then return false fi;
od
end proc:
select(filter, [seq(i, i=2..10^6, 6)]);
CROSSREFS
Cf. A356077.
Sequence in context: A012998 A143760 A064605 * A295373 A356746 A132039
KEYWORD
nonn,more
AUTHOR
J. M. Bergot and Robert Israel, Jul 27 2022
STATUS
approved