A356108 Numbers == 2 (mod 6) that cannot be written as p^2 + q where p and q are primes.

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.

Links

Table of n, a(n) for n=1..8.

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

Adjacent sequences: A356105 A356106 A356107 * A356109 A356110 A356111

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Jul 27 2022

Status

approved