A296012 Primes of the form k + k+1 + k+2 +-1 where k, k+1, and k+2 are all composite numbers.

79, 101, 103, 149, 151, 167, 191, 193, 227, 229, 257, 277, 281, 283, 347, 349, 353, 359, 367, 373, 401, 431, 433, 439, 461, 463, 479, 509, 557, 563, 607, 613, 617, 619, 641, 643, 647, 653, 659, 661, 709, 733, 739, 743, 761, 797, 821, 823, 857, 859, 863, 887, 907, 911, 967, 971, 977, 983, 1019, 1021

Offset: 1

Author

Martin Michael Musatov, Dec 02 2017

Keywords

• nonn

Comments

Primes p such that floor((p-2)/3) and floor((p-2)/3)+2 are composite. - Robert Israel, Dec 03 2017

Examples

			25 + 26 + 27 + 1 = 79,
33 + 34 + 35 - 1 = 101,
33 + 34 + 35 + 1 = 103, etc.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A136799.

Programs

Maple

filter:= proc(n) local k;
  if not isprime(n) then return false fi;
  k:= floor((n-2)/3);
  not isprime(k) and not isprime(k+1) and not isprime(k+2)
end proc:
select(filter, [seq(i,i=5..2000, 2)]); # Robert Israel, Dec 03 2017

Mathematica

Select[Join @@ Map[{{Total@ # - 1, #}, {Total@ # + 1, #}} &, Partition[Range@ 350, 3, 1]], And[PrimeQ@ First@ #, AllTrue[Last@ #, CompositeQ]] &][[All, 1]] (* Michael De Vlieger, Dec 03 2017 *)

Python

from _future_ import division
from sympy import nextprime, isprime
A296012_list, p = [], 2
while len(A296012_list) < 10000:
    k = (p-2)//3
    if not (isprime(k) or isprime(k+2)):
        A296012_list.append(p)
    p = nextprime(p) # Chai Wah Wu, Jan 24 2018