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A338416 Numbers k such that both 3*k-2 and 2*k-3 are in A338410.

%I A338416 #15 May 20 2023 10:20:00
%S A338416 11,71,1091,2927,7127,12347,23087,41651,56951,74747,119771,234947,
%T A338416 298451,405287,458207,649907,656291,708371,936587,991187,1015127,
%U A338416 1056971,1058807,1128527,1129787,1169687,1393967,1413371,1417067,1442351,1502747,1707551,1752227,1785071,1928807,1957871,1998947
%N A338416 Numbers k such that both 3*k-2 and 2*k-3 are in A338410.
%C A338416 Primes p such that 3*p-2, 2*p-3, (3*p+1)/2 and (2*p-1)/3 are all prime.
%C A338416 All terms == 11 (mod 12).
%H A338416 Robert Israel, <a href="/A338416/b338416.txt">Table of n, a(n) for n = 1..4000</a>
%e A338416 a(3) = 1091 is in the sequence because 3*1091-2=3271 and 2*1091-3=2179 are in A338410.
%p A338416 filter:= proc(p) isprime(p) and isprime(3*p-2) and isprime(2*p-3) and isprime((3*p+1)/2) and isprime((2*p-1)/3) end proc:
%p A338416 select(filter, [seq(i,i=11 .. 10^7, 12)]);
%t A338416 Select[Prime[Range[150000]],AllTrue[{3#-2,2#-3,(2#-1)/3,(3#+1)/2},PrimeQ]&] (* _Harvey P. Dale_, May 20 2023 *)
%Y A338416 Cf. A338410.
%K A338416 nonn
%O A338416 1,1
%A A338416 _J. M. Bergot_ and _Robert Israel_, Oct 25 2020