|
%I #16 Aug 17 2024 14:20:11
%S 44,102,104,108,152,188,226,234,296,328,426,526,586,692,720,842,846,
%T 856,926,994,1076,1278,1284,1386,1426,1484,1498,1574,1704,1746,1764,
%U 1822,1826,1848,1952,2058,2114,2128,2142,2148,2164,2186,2386,2416,2442,2484,2640,2704,2904,2948,3108,3142,3164
%N Numbers k such that k^2 + 1, k^2 + 3 and k^2 + 5 are semiprimes.
%C All terms are even.
%C a(n)^2 + 3 or a(n)^2 + 5 is 3 times a prime. In the first case, a(n)/3 is in A111051.
%H Robert Israel, <a href="/A375390/b375390.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 104 is a term because 104^2 + 1 = 10817 = 29 * 373, 104^2 + 3 = 10819 = 31 * 349 and 104^2 + 5 = 10821 = 3 * 3607 are all semiprimes.
%p select(t -> andmap(s -> numtheory:-bigomega(t^2+s)=2, [1,3,5]), 2*[$1..2000]);
%t Select[Range[3000], 2 == PrimeOmega[1 + #^2] == PrimeOmega[3 +
%t #^2] == PrimeOmega [5 + #^2] &]
%Y Cf. A001358, A111051. Intersection of A085722, A242331 and A242333.
%K nonn,new
%O 1,1
%A _Zak Seidov_ and _Robert Israel_, Aug 15 2024
|
