A375390 Numbers k such that k^2 + 1, k^2 + 3 and k^2 + 5 are semiprimes.

44, 102, 104, 108, 152, 188, 226, 234, 296, 328, 426, 526, 586, 692, 720, 842, 846, 856, 926, 994, 1076, 1278, 1284, 1386, 1426, 1484, 1498, 1574, 1704, 1746, 1764, 1822, 1826, 1848, 1952, 2058, 2114, 2128, 2142, 2148, 2164, 2186, 2386, 2416, 2442, 2484, 2640, 2704, 2904, 2948, 3108, 3142, 3164

Offset: 1

Author

Zak Seidov and Robert Israel, Aug 15 2024

Keywords

• nonn

Comments

All terms are even.

a(n)^2 + 3 or a(n)^2 + 5 is 3 times a prime. In the first case, a(n)/3 is in A111051.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A111051. Intersection of A085722, A242331 and A242333.

Programs

Maple

select(t -> andmap(s -> numtheory:-bigomega(t^2+s)=2, [1,3,5]), 2*[$1..2000]);

Mathematica

Select[Range[3000], 2 == PrimeOmega[1 + #^2] == PrimeOmega[3 +
#^2] ==   PrimeOmega [5 + #^2] &]