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A328160 Terms k of A112998 such that k+2 is nonsquarefree.

%I A328160 #15 Apr 20 2023 02:11:11
%S A328160 61,73,277,421,2797,6217,8521,9277,9817,10357,11161,12301,12841,13381,
%T A328160 15121,17377,17881,18097,19861,25657,30517,30661,33037,35521,36241,
%U A328160 36457,48121,50821,51481,54421,56437,58417,60217,66601,66697,67057,71341,74077,77641,79801,88117,94777,96181,98017
%N A328160 Terms k of A112998 such that k+2 is nonsquarefree.
%C A328160 Complement of A328137 in A112998.
%C A328160 Each term is either 3*x^2-2 where x, 3*x^2-2 and (3*x^2-1)/2 are prime or it is 9*x-2 where x, 9*x-2 and (9*x-1)/2 are prime.
%H A328160 Robert Israel, <a href="/A328160/b328160.txt">Table of n, a(n) for n = 1..7487</a>
%e A328160 a(3)=277 is a term because 277 is prime, 277+1=2*139 where 139 is prime, and 279=3^2*31 is a 3-almost prime that is nonsquarefree.
%p A328160 N:= 100000:
%p A328160 A1:= map(x -> 3*x^2-2, select(x -> isprime(x) and isprime(3*x^2-2) and isprime((3*x^2-1)/2), {seq(i,i=3..floor(sqrt((N+2)/3)),2)})):
%p A328160 A2:= map(x -> 9*x-2, select(x -> isprime(x) and isprime(9*x-2) and isprime((9*x-1)/2), {seq(i,i=3..(N+2)/9,2)})):
%p A328160 sort(convert(A1 union A2,list));
%t A328160 Select[Prime@ Range[10^4], And[PrimeOmega /@ {# + 1, # + 2} == {2, 3}, ! SquareFreeQ[# + 2]] &] (* _Michael De Vlieger_, Oct 06 2019 *)
%Y A328160 Cf. A112998, A328137.
%K A328160 nonn
%O A328160 1,1
%A A328160 _Robert Israel_, Oct 05 2019