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 A247695 #27 Aug 06 2020 04:23:56
%S A247695 34867,370740,4087295,19027947
%N A247695 Minimal absolute discriminants a(n) of complex quadratic fields with 3-class group of type (3,3), 3-principalization type E.8 (2234), and second 3-class group G of odd nilpotency class cl(G)=2(n+2)+1.
%C A247695 The 3-principalization type (transfer kernel type, TKT) E.8 (2234) is not a permutation and has three fixed points.
%C A247695 The nilpotency condition cl(G)=2n+5 for the second 3-class group is equivalent to a transfer target type, TTT (called IPAD by Boston, Bush and Hajir) of the shape [(3,9),(3^{n+2},3^{n+3}),(3,9)^2].
%C A247695 The second 3-class group G is a vertex of depth 1 on the coclass tree with root SmallGroup(243,8) contained in the coclass graph G(3,2).
%C A247695 All these fields possess a Hilbert 3-class field tower of exact length 3.
%C A247695 A247695 is an extremely sparse subsequence of A242878 and it is exceedingly hard to compute a(n) for n>0.
%H A247695 N. Boston, M. R. Bush and F. Hajir, <a href="http://arxiv.org/abs/1111.4679">Heuristics for p-class towers of imaginary quadratic fields</a>, Preprint: arXiv:1111.4679v1 [math.NT], 2011, Math. Ann. (2013).
%H A247695 M. R. Bush and D. C. Mayer, <a href="http://arxiv.org/abs/1312.0251">3-class field towers of exact length 3</a>, Preprint: arXiv:1312.0251v1 [math.NT], 2013.
%H A247695 D. C. Mayer, <a href="https://doi.org/10.1142/S179304211250025X">The second p-class group of a number field</a>, Int. J. Number Theory 8 (2) (2012), 471-505.
%H A247695 D. C. Mayer, <a href="http://arxiv.org/abs/1403.3899">The second p-class group of a number field</a>, arXiv:1403.3899 [math.NT], 2014.
%H A247695 D. C. Mayer, <a href="https://doi.org/10.1007/s00605-010-0277-x">Transfers of metabelian p-groups</a>, Monatsh. Math. 166 (3-4) (2012), 467-495.
%H A247695 D. C. Mayer, <a href="http://arxiv.org/abs/1403.3896">Transfers of metabelian p-groups</a>, arXiv:1403.3896 [math.GR], 2014.
%H A247695 D. C. Mayer, <a href="https://doi.org/10.5802/jtnb.842">The distribution of second p-class groups on coclass graphs</a>, J. Théor. Nombres Bordeaux 25 (2) (2013), 401-456.
%H A247695 D. C. Mayer, <a href="http://arxiv.org/abs/1403.3833">The distribution of second p-class groups on coclass graphs</a>, arXiv:1403.3833 [math.NT], 2014.
%H A247695 D. C. Mayer, <a href="http://arxiv.org/abs/1403.3839">Principalization algorithm via class group structure</a>, Preprint: arXiv:1403.3839v1 [math.NT], 2014.
%H A247695 Daniel C. Mayer, <a href="https://arxiv.org/abs/1504.00851">Periodic sequences of p-class tower groups</a>, arXiv:1504.00851 [math.NT], 2015.
%H A247695 Wikipedia, <a href="https://en.wikipedia.org/wiki/Artin_transfer_(group_theory)#Example">Artin transfer (group theory), Table 2</a>
%e A247695 For a(0)=34867, we have the ground state of TKT E.8 with TTT [(3,9),(9,27),(3,9)^2] and cl(G)=5.
%e A247695 For a(1)=370740, we have the first excited state of TKT E.8 with TTT [(3,9),(27,81),(3,9)^2] and cl(G)=7.
%e A247695 a(0) and a(1) are due to D. C. Mayer (2012).
%e A247695 a(2) and a(3) are due to N. Boston, M. R. Bush and F. Hajir (2013).
%Y A247695 Cf. A242862, A242863, A242878 (supersequences), A247692, A247693, A247694, A247696, A247697 (disjoint sequences).
%K A247695 hard,more,nonn
%O A247695 0,1
%A A247695 _Daniel Constantin Mayer_, Sep 28 2014