A001682

[Emeric Deutsch]

RKG:
With Maple I have derived the following terms <=3000:

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, 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, 2272, 2293,
2316, 2337, 2360, 2381, 2402, 2425, 2446, 2469, 2490, 2513, 2534, 2555,
2578, 2599, 2622, 2643, 2666, 2687, 2708, 2731, 2752, 2775, 2796, 2819,
2840, 2861, 2884, 2905, 2928, 2949, 2972, 2993

This list agrees with the terms you have found.
Emeric

On Wed, 9 Mar 2005, Richard Guy wrote:

> 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.
>