A395198 - OEIS

%I #21 Apr 21 2026 15:32:20

%S 6,30,36,54,114,120,210,510,546,660,804,810,1056,1170,1356,1686,1764,

%T 1884,1926,2394,3066,3330,3396,4110,4884,5034,5250,6054,8514,9024,

%U 9270,9540,10374,11646,11844,13350,13764,14310,14376,15756,16470,16644,17424,17526,18906,21420,21894,23154,23220,24204

%N Numbers k such that 2*k +- 1 and 5*k +- 1 are twin prime pairs.

%C All terms are divisible by 6.

%H Robert Israel, <a href="/A395198/b395198.txt">Table of n, a(n) for n = 1..10000</a>

%e a(5) = 114 is a term because 2*114-1 = 227, 2*114+1 = 229, 5*114-1 = 569 and 5*114+1 = 571 are all prime.

%p filter:= proc(n) andmap(isprime,[2*n-1,2*n+1,5*n-1,5*n+1]) end proc:

%p select(filter, [seq(i,i = 6..30000, 6)]);

%t Select[Range[6, 30000, 6], AllTrue[{2*#-1, 2*#+1, 5*#-1, 5*#+1}, PrimeQ] &] (* _Paolo Xausa_, Apr 21 2026 *)

%o (PARI) first(nn)= my(r=List()); forstep(t=6, oo, 6, if(isprime(2*t-1) && isprime(5*t-1) && isprime(2*t+1) && isprime(5*t+1), listput(~r, t); #r<nn || break)); Vec(r); \\ _Ruud H.G. van Tol_, Apr 21 2026

%Y Intersection of A040040 and A153877.

%K nonn

%O 1,1

%A _Will Gosnell_ and _Robert Israel_, Apr 15 2026