A354834 Numbers k such that 2*k can be written in at least one way as p+q with p, q, p+2*q and 2*q+p all prime.

4, 5, 6, 8, 9, 10, 12, 15, 18, 21, 25, 27, 28, 30, 33, 35, 36, 38, 39, 42, 45, 48, 50, 51, 54, 57, 60, 63, 66, 72, 75, 78, 80, 81, 84, 85, 87, 88, 90, 93, 98, 99, 102, 105, 108, 111, 113, 114, 115, 117, 120, 123, 126, 129, 132, 135, 138, 140, 141, 144, 147, 150, 153, 155, 156, 159, 162, 165, 168

Offset

1,1

Comments

Numbers k such that A237885(k) > 0.

If k is not divisible by 3, then p or q must be 3.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 6 is a term because 2*6 = 12 = 5+7 with 5, 7, 5+2*7 = 19 and 2*5+7 = 17 all prime.

Maple

N:= 1000: # for terms <= N
S:= {}:
P:= select(isprime, [seq(i, i=3..2*N, 2)]):
nP:= nops(P):
for i from 1 to nP do
  p:= P[i];
  for j from i+1 to nP do
    q:= P[j];
    if p+q > 2*N then break fi;
    r:= (p+q)/2;
    if isprime(p+2*q) and isprime(2*p+q) then
      S:= S union {r}
    fi
  od
od:
sort(convert(S, list));

Crossrefs

Cf. A237885.

Sequence in context: A023851 A285279 A091242 * A089585 A089253 A047432

Adjacent sequences: A354831 A354832 A354833 * A354835 A354836 A354837

Keyword

nonn

Author

Robert Israel, Jun 07 2022

Status

approved