A355518 Primes that cannot be represented as 2*p - q where p, q and 2*p^2 - q^2 are prime.

2, 3, 5, 13, 17, 37, 61, 137

Offset

1,1

Comments

Conjecture: there are no other terms.

Links

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

Example

11 is not in the sequence because 11 = 2*7 - 3 with 7, 3 and 2*7^2 - 3^2 = 89 prime.

Maple

M:= 10000: # to get all terms <= M
Pmax:= floor(M/(2-sqrt(2))):
Qmax:= floor(sqrt(2)*Pmax):
Q:= select(isprime, [2, seq(i, i=3..Qmax, 2)]):
P:= select(`<=`, Q, Pmax): nQ:= nops(Q):
S:= convert(select(`<=`, P, M), set):
for p in P  do
  for j from 1 to nQ do
    q:= Q[j];
    r:= 2*p^2-q^2;
    if r < 2 then break fi;
    s:= 2*p-q;
    if s <= M and isprime(r) and isprime(s) then S:= S minus {s} fi;
od od:
S;

Crossrefs

Cf. A355521.

Sequence in context: A065820 A163268 A235624 * A108562 A087523 A073919

Adjacent sequences: A355515 A355516 A355517 * A355519 A355520 A355521

Keyword

nonn

Author

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

Status

approved