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EXAMPLE
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For n >= 3, the cycle graph is minimally 1-tough. For 3 <= n <= 6, this is the only minimally 1-tough graph, so a(n) = 1.
For n = 7 and n = 8, the graphs with House of Graphs id's 536 and 36063, respectively, are also minimally 1-tough, and a(7) = a(8) = 2.
For n = 9, the a(9) = 5 minimally 1-tough graphs are (in graph6 format) "H?CidB?" (9-cycle), "H?Cicr_", "H?Ci[b_", "H?Ci[^o", and "H?KqKVO".
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