A382049 Numbers k such that k +- 2 and k +- 3 are all semiprimes.

12, 36, 216, 540, 1044, 4284, 6336, 11304, 17640, 30276, 31284, 34056, 35496, 35820, 37836, 41796, 46080, 47664, 50940, 57240, 62244, 71064, 75096, 80856, 84924, 98820, 100044, 103536, 106344, 143100, 143424, 144936, 149220, 159264, 159804, 162036, 168120, 172584, 175176, 177624, 194760, 195300

Offset: 1

Author

Zak Seidov and Robert Israel, Mar 13 2025

Keywords

• nonn

Comments

Except for a(1) = 12, these are the numbers k divisible by 36 with (k +- 2)/2 and (k +- 3)/3 prime.

Examples

			a(3) = 216 is a term because 216 - 3 = 213 = 3 * 71, 216 - 2 = 215 = 2 * 107, 216 + 2 = 218 = 2 * 109, and 216 + 3 = 219 = 3 * 73 are all semiprimes.
		

Links

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

Crossrefs

Cf. A001358, A105571.

Programs

Maple

filter:= proc(n) andmap(isprime, [(n-3)/3, (n-2)/2,(n+2)/2,(n+3)/3]) end proc:
filter(12):= true:
S:= select(filter, [12, seq(i,i=36 .. 10^6, 36)]):

Mathematica

Select[Range[12, 200000], 2 ==  PrimeOmega[# - 2] ==
PrimeOmega[# + 2] ==  PrimeOmega[# - 3] == PrimeOmega[# + 3] &]