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 A362015 #13 Apr 06 2023 08:29:25 %S A362015 1,2,4,6,3,9,8,12,15,5,10,20,25,18,30,35,7,14,21,28,42,49,40,56,45,63, %T A362015 50,70,77,11,22,33,44,55,66,88,99,110,121,84,132,91,13,26,39,52,65,78, %U A362015 104,117,130,143,156,169,98,154,182,165,195,176,208,105,187,17,34,51,68,85,102,119,136 %N A362015 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that, given the list of primes that form the factors of all previous terms a(1)..a(n-1), is a multiple of the prime in that list which is a factor of the fewest previous terms. If two or more such primes exist the smallest is chosen. %C A362015 After 5 million terms the lowest number not to have appeared is 16 = 2^4. In that range 2 is a factor of 2614180 terms while 3 is a factor of 1763610 terms. As these are the most and second-most common prime factors this suggest that 16, and other higher powers of 2, will never appear as that would require 2 to be the least common factor of all previous terms. This is also true for the powers of the other smaller primes. %C A362015 In the first 5 million terms the only fixed point, other than the first two terms, is 4175, although it is probable that more exist. %H A362015 Scott R. Shannon, <a href="/A362015/b362015.txt">Table of n, a(n) for n = 1..10000</a> %H A362015 Scott R. Shannon, <a href="/A362015/a362015.png">Image of the first 100000 terms</a>. The green line is a(n) = n. %H A362015 Scott R. Shannon, <a href="/A362015/a362015_1.png">Image of the first 5000000 terms</a> %e A362015 a(5) = 3 as the list of primes that divide all previous terms a(1)..a(4) is 2 and 3, with 2 being a factor of three terms and 3 being a factor of one term. Therefore a(5) is the lowest multiple of 3 that has not appeared, which is 3. %Y A362015 Cf. A361372, A351495, A359804, A353026, A352793. %K A362015 nonn,look %O A362015 1,2 %A A362015 _Scott R. Shannon_, Apr 03 2023