A368615 - OEIS

%I #13 Jan 12 2024 22:46:27

%S 58,74,166,226,262,326,334,478,566,694,734,802,838,886,1114,1142,1294,

%T 1382,1514,1574,1894,2038,2078,2138,2858,3254,3274,3314,3578,4286,

%U 4306,4426,5102,5242,5386,5398,5578,5806,5906,6022,6046,6362,6866,7094,7142,7246,7274,7438,7694,7838,7886,7934

%N Semiprimes k such that prime(k) - k and prime(k) + k are also semiprimes.

%C All terms are even.

%H Robert Israel, <a href="/A368615/b368615.txt">Table of n, a(n) for n = 1..10000</a>

%F Numbers k such that A001222(k) = A001222(A000040(k) - k) = A001222(A000040(k) + k) = 2.

%F a(n) == 2 (mod 4). - _Hugo Pfoertner_, Jan 05 2024

%e a(3) = 166 is a term because the 166th prime is 983, and 166 = 2 * 83, 983 - 166 = 817 = 19 * 43, and 983 + 166 =  1149 = 3 * 383 are all semiprimes.

%p p:= 1: R:= NULL: count:= 0:

%p for k from 2 by 2 while count < 100 do

%p   p:= nextprime(nextprime(p));

%p   if isprime(k/2) and numtheory:-bigomega(k+p) = 2 and numtheory:-bigomega(p-k) = 2 then count:= count+1; R:= R,k fi

%p od:

%p R;

%t s = {}; Do[If[{2, 2, 2} == PrimeOmega[{k, Prime[k] + k, Prime[k] - k}], AppendTo[s, k]], {k, 4, 10000}]; s

%Y Cf. A000040, A001222, A001358.

%K nonn

%O 1,1

%A _Zak Seidov_ and _Robert Israel_, Dec 31 2023