A296012 - OEIS

%I #26 Jan 26 2018 08:32:21

%S 79,101,103,149,151,167,191,193,227,229,257,277,281,283,347,349,353,

%T 359,367,373,401,431,433,439,461,463,479,509,557,563,607,613,617,619,

%U 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

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

%C Primes p such that floor((p-2)/3) and floor((p-2)/3)+2 are composite. - _Robert Israel_, Dec 03 2017

%H Chai Wah Wu, <a href="/A296012/b296012.txt">Table of n, a(n) for n = 1..10000</a>

%e 25 + 26 + 27 + 1 = 79,

%e 33 + 34 + 35 - 1 = 101,

%e 33 + 34 + 35 + 1 = 103, etc.

%p filter:= proc(n) local k;

%p   if not isprime(n) then return false fi;

%p   k:= floor((n-2)/3);

%p   not isprime(k) and not isprime(k+1) and not isprime(k+2)

%p end proc:

%p select(filter, [seq(i,i=5..2000, 2)]); # _Robert Israel_, Dec 03 2017

%t 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 *)

%o (Python)

%o from __future__ import division

%o from sympy import nextprime, isprime

%o A296012_list, p = [], 2

%o while len(A296012_list) < 10000:

%o     k = (p-2)//3

%o     if not (isprime(k) or isprime(k+2)):

%o         A296012_list.append(p)

%o     p = nextprime(p) # _Chai Wah Wu_, Jan 24 2018

%Y Cf. A000045, A136799.

%K nonn

%O 1,1

%A _Martin Michael Musatov_, Dec 02 2017