A355521 Primes that cannot be represented as 2*p+q where p, q and (2*p^2+q^2)/3 are prime.

2, 3, 5, 7, 13, 31, 37, 97, 211, 271

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.

Links

Table of n, a(n) for n=1..10.

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

Cf. A355518.

Sequence in context: A067573 A103199 A054217 * A048414 A048399 A249692

Adjacent sequences: A355518 A355519 A355520 * A355522 A355523 A355524

Keyword

nonn

Author

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

Status

approved