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

1,1

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.

Links

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

Example

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.

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] &]

Crossrefs

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

Sequence in context: A044563 A129289 A039527 * A253391 A050944 A332590

Adjacent sequences: A375387 A375388 A375389 * A375391 A375392 A375393

Keyword

nonn

Author

Zak Seidov and Robert Israel, Aug 15 2024

Status

approved