This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382049 #7 Mar 14 2025 20:23:19 %S A382049 12,36,216,540,1044,4284,6336,11304,17640,30276,31284,34056,35496, %T A382049 35820,37836,41796,46080,47664,50940,57240,62244,71064,75096,80856, %U A382049 84924,98820,100044,103536,106344,143100,143424,144936,149220,159264,159804,162036,168120,172584,175176,177624,194760,195300 %N A382049 Numbers k such that k +- 2 and k +- 3 are all semiprimes. %C A382049 Except for a(1) = 12, these are the numbers k divisible by 36 with (k +- 2)/2 and (k +- 3)/3 prime. %H A382049 Robert Israel, <a href="/A382049/b382049.txt">Table of n, a(n) for n = 1..10000</a> %e A382049 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. %p A382049 filter:= proc(n) andmap(isprime, [(n-3)/3, (n-2)/2,(n+2)/2,(n+3)/3]) end proc: %p A382049 filter(12):= true: %p A382049 S:= select(filter, [12, seq(i,i=36 .. 10^6, 36)]): %t A382049 Select[Range[12, 200000], 2 == PrimeOmega[# - 2] == %t A382049 PrimeOmega[# + 2] == PrimeOmega[# - 3] == PrimeOmega[# + 3] &] %Y A382049 Cf. A001358, A105571. %K A382049 nonn %O A382049 1,1 %A A382049 _Zak Seidov_ and _Robert Israel_, Mar 13 2025