Appendix I:  Why Were 35, 91, and 95 Treated Differently?

It's intriguing to consider the following table:

           Double-Triangular and Related Numbers

     k     T = (k+2)(k+3)     Q = 6k+1     T-Q      TQ
    ---    --------------    ----------   ------   -----
     1          12*              7           5       35
     2          20*             13           7       91
     3          30*             19          11      209
     4          42*            [25]         17
     5          56*             31         [25]
     6          72              37         (35)
     7          90              43          47
     8         110             [49]         61
     9         132             (55)        (77)
    10         156              61         (95)
    11         182              67
    12         210              73
    13         240             (85)
    14         272             (91)
    15         306              97
    16         342             103
    18         420             109


Notice that the values of TQ less than 100 are precisely those 
that are treated by arithmetic-harmonic decomposition in the 2/n 
table.  Also, I've placed parentheses around the composite values 
in the Q and T-Q columns, with square brackets to indicate 
squares.  Notice that the numbers 35, 91, and 95 appear, as 
do the corresponding values of 2a-p, namely, the squares 25, 
49, and 25 respectively.  Also, the number 55 appears, which
was treated in a slightly unusual way in the 2/n table by being
sieved out by the larger of its two divisors, rather than the 
smaller.  The only other composites in these columns are 77 and
85, which don't seem to have been treated in any unusual way in
the 2/n table.  By the way, the numbers in the T column, which
are double-triangular numbers, seem to have been favorite choices
for "a".  Each value marked with asterisk was used in the 2/n 
table as an "a" value at least once.