A367496 Semiprimes k such that 2*k - 1 and 2*k + 1 are also semiprimes.

25, 46, 93, 118, 133, 145, 161, 206, 226, 235, 259, 267, 291, 295, 334, 335, 361, 377, 395, 407, 447, 497, 529, 573, 579, 583, 669, 674, 685, 694, 695, 781, 843, 898, 899, 921, 926, 961, 979, 1059, 1079, 1114, 1115, 1142, 1159, 1214, 1227, 1241, 1257, 1285, 1286, 1294, 1315, 1379, 1393, 1405

Offset: 1

Author

Zak Seidov and Robert Israel, Nov 20 2023

Keywords

• nonn

Comments

One of the three semiprimes k, 2*k - 1 and 2*k + 1 is 3 times a prime.

Examples

			a(3) = 93 is a term because 93 = 3 * 31, 2 * 93 - 1 = 185 = 5 * 37 and 2 * 93 + 1 = 187 = 11 * 17 are semiprimes.
		

Links

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

Crossrefs

Cf. A001358. Intersection of A111153 and A111168.

Programs

Maple

select(t -> numtheory:-bigomega(t) = 2 and numtheory:-bigomega(2*t-1) = 2 and numtheory:-bigomega(2*t+1) = 2, [$1..2000]);

Mathematica

Select[Range[1410],PrimeOmega[#]==PrimeOmega[2#+1]==PrimeOmega[2#-1]==2 &] (* Stefano Spezia, Nov 20 2023 *)