A001682

[Richard Guy]

I'm collecting Murray Klamkin problems
for a book, and have reached Amer
Math Monthly 64(1957) 665 where Joe
Lipman solves a Murray problem
``as long as tables of sufficient
accuracy are available.''

Of course, we don't use tables any more.
I've corrected the arithmetic in the
original, and in so doing am able to make
a modest addition to A001682 which
currently reads

21,42,65,86,109,130,151,174,195,218,239,262,283,
304,327,348,371,392,415,436,457,480,501,524,545,
568,589,610,633,654,677,698,721,742,763

and to which may be added

786,807, 830, 851, 874, 895, 916, 939,
     960, 983,1004,1027,1048,1069,1092,
    1113,1136,1157,1180,1201,1222,1245,
    1266,1289,1310,1333,1354,1375,1398,
    1419,1442,1463,1486,1507,1528,1551,
    1572,1595,1616.1639,1660,1681,1704,
    1725,1748,1769,1792,1813,1834,1857,
    1878,1901,1922,1945,1966,1987,2010,
    2031,2054,2075,2098,2119,2140,2163,
    2184,2207,2228,2249 (not 2251)
where I've continued the calculation
until the difference pattern
   21   23   21   23   21   21   23
is broken.  What's the magic number
whose continued fraction expansion
will tell me when to make a gear
change?

As always, someone should check
my hand calculations!    R.