OFFSET

1,1

COMMENTS

2*p^2+q^2 is always divisible by 3 when neither p nor q is divisible by 3.

Conjecture: there are no other terms.

EXAMPLE

11 is not in the sequence because 11 = 2*2+7 with 2, 7 and (2*2^2+7^2)/3 = 19 prime.

MAPLE

M:= 50000:

Pr:= select(isprime, [2, seq(i, i=5..M, 2)]):

nP:= nops(Pr):

S:= convert(Pr, set) union {3}:

for p in Pr do

if 2*p+2 > M then break fi;

for q in Pr do

r:= 2*p+q;

if r > M then break fi;

if isprime(r) and isprime((2*p^2+q^2)/3) then

S:= S minus {r}

fi

od od:

S;

CROSSREFS

KEYWORD

nonn

AUTHOR

J. M. Bergot and Robert Israel, Jul 05 2022

STATUS

approved