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 A337181 #13 Feb 14 2021 13:17:34 %S A337181 1,2,4,8,12,6,9,18,24,16,20,10,25,30,15,27,36,42,14,21,28,48,32,40,44, %T A337181 22,52,26,56,60,35,45,50,54,64,66,68,34,72,51,63,81,84,78,39,90,65,70, %U A337181 75,80,96,76,38,88,92,46,100,104,108,102,99,33,117,126,91,49,98,112,116,58,120 %N A337181 a(1) = 1, a(2) = 2; for n>2, a(n) is the smallest number not already used that is a multiple of at least one prime factor of both a(n-1) and a(n-2). %C A337181 As each term must have at least two prime factors no term, other than the initial 2, can be prime. %H A337181 Scott R. Shannon, <a href="/A337181/a337181.png">Image of the terms for n=1..500000</a>. The green line is a(n) = n, indicating the other lines are slightly curved downward. %e A337181 a(4) = 8 as the factors of a(4-2) = a(2) = 2 and a(4-1) = a(3) = 4 = 2*2, thus a(4) must be the minimum unused multiple of 2*2 = 4, which is 8. %e A337181 a(6) = 6 as the factors of a(6-2) = a(4) = 8 = 2*2*2 and a(6-1) = a(5) = 12 = 2*2*3, thus a(4) must be the minimum unused multiple of 2*2 = 4 or 2*3 = 6. As 4 has been used a(6) = 6. %e A337181 a(13) = 25 as the factors of a(13-2) = a(11) = 20 = 2*2*5 and a(13-1) = a(12) = 10 = 2*5, thus a(13) must be the minimum unused multiple of 2*2 = 4, 2*5 = 10, or 5*5 = 25. As 4,8,10,12,16,20,24 have been used, a(13) = 25. %Y A337181 Cf. A064413, A336957, A098550, A270139. %K A337181 nonn %O A337181 1,2 %A A337181 _Scott R. Shannon_, Jan 28 2021