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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000045, A136799.

Sequence in context: A285228 A087537 A117840 * A193142 A033250 A139922

Adjacent sequences: A296009 A296010 A296011 * A296013 A296014 A296015

Keyword

nonn

Author

Martin Michael Musatov, Dec 02 2017

Status

approved