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Orders of consecutive clusters of non-Chen primes.
1

%I #24 Mar 05 2017 05:39:21

%S 1,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,2,1,1,1,1,1,3,1,1,2,1,1,3,

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,2,1,2,1,1,3,1,2,1,1,1,2

%N Orders of consecutive clusters of non-Chen primes.

%H Charles R Greathouse IV, <a href="/A280010/b280010.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1)=1 since the first cluster consists of the single value p=43.

%e a(3)=2 since the third cluster consists of the consecutive non-Chen primes {73,79}.

%t Length /@ DeleteCases[Split@ Table[Boole@ Nand[# != 1, PrimeOmega@ # <= 2] &[# + 2] &@ Prime@ n, {n, 300}], k_ /; Total@ k == 0] (* _Michael De Vlieger_, Feb 27 2017 *)

%o (PARI) do(lim)=my(v=List(), u=v, r, s); forprime(p=2, lim\2, forprime(q=2, min(lim\p, p), listput(u, p*q))); u=Set(u); r=3; forprime(p=5, lim, if(p-r==2 || setsearch(u, r+2), if(s, listput(v, s); s=0), s++); r=p); u=0; Vec(v) \\ _Charles R Greathouse IV_, Feb 27 2017

%Y Cf. A102540, A280009.

%K nonn

%O 1,3

%A _Enrique Navarrete_, Feb 21 2017