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 A232832 #18 Dec 06 2015 22:41:58 %S A232832 1,2,4,5,7,8,13,15 %N A232832 Shortest composition length for a finite solvable group of derived length n. %C A232832 The composition length of a finite solvable group is equal to the number of prime factors of the order, counting multiplicities. Thus, for example, the symmetric group of permutations on 4 elements is a solvable group of derived length 3, and its order is 24=2*2*2*3 which has 4 prime divisors. This is the smallest possible number of factors for a solvable group of derived length 3, so a(3) = 4. %C A232832 The sequences is monotonic increasing, and the difference cannot be 1 twice in a row. Thus the smallest possible differences are 1,2,1,2.., which is what we see for the first 5 differences. The sixth difference is 5 which breaks that pattern. Glasby shows that a(n) grows exponentially, with exponent at least 1.3, so in the long run the differences must often be very large. However, it seems that the difference 1 may show up infinitely often. %H A232832 S. P. Glasby, <a href="http://dx.doi.org/10.1515/jgth.2005.8.3.339">Solvable groups with a given solvable length, and minimal composition length</a>, Journal of Group Theory, vol 8, issue 3, May 2005 %Y A232832 Cf. A104114. %K A232832 nonn,more %O A232832 1,2 %A A232832 _Moshe Shmuel Newman_, Nov 30 2013