Partial-Sum -> Some Primes

[Hans Havermann]

> Also by hand, so please check
> 1 2 4 3 6 5 12 7 20 9 8 21 24 10 16 25 18 ...
>
> the sequence of primes may be of interest
> (1) 5 17 29 59 89 173 229 409 499 587 839 1151 1291 1531 1931 2237 ...


Mathematica coding done by hand. Caveat emptor. :)

1, 2, 4, 3, 6, 5, 12, 7, 16, 9, 14, 13, 8, 11, 10, 17, 18, 15, 22, 24, 
20, 23, 26, 25, 30, 28, 32, 33, 38, 29, 48, 27, 34, 44, 36, 19, 42, 47, 
52, 35, 50, 21, 56, 53, 46, 39, 60, 45, 54, 31, 40, 37, 58, 49, 70, 55, 
68, 61, 72, 43, 98, 41, 74, 57, 84, 59, 78, 64, 82, 63, 108, 51, 88, 
76, 90, 75, 66, 79, 102, 69, 94, 67, 114, 73, 92, 80, 100, 62, 86, 87, 
128, 77, 116, 65, 104, 71, 120, 97, 110, 81, 96, 89, 112, 91, 136, 99, 
126, 85, 132, 113, 106, 101, 134, 93, 122, 105, 142, 103, 148, 109, 
118, ...

(1), 5, 17, 29, 59, 89, 173, 229, 373, 463, 617, 773, 877, 1031, 1181, 
1453, 1759, 2029, 2447, 2927, 3347, 3853, 4451, 5051, 5801, 6529, 7393, 
8317, 9419, 10289, 11777, 12641, 13763, 15259, 16519, 17203, 18757, 
20543, 22571, 23971, 26021, 26903, 29311, 31643, 33713, 35507, 38327, 
40487, 43133, 44683, 46723, 48647, 51721, 54367, 58217, 61297, 65173, 
68711, 72959, 75539, 81517, 84059, 88721, 92369, 97829, 101723, 106949, 
111301, 116959, 121369, 129037, 132709, 139133, 144757, 151507, 157207, 
162289, 168451, 176509, 182029, 189643, 195137, 204599, 210731, 218551, 
225431, 234131, 239587, 247241, 255071, 266719, 273803, 284591, 290701, 
300581, 307397, 319037, 328543, 339433, 347533, 357229, 366307, 377843, 
387307, 401587, 412081, 425563, 434743, 449131, 461561, 473327, 484639, 
499781, 510383, 524413, 536593, 553207, 565361, 582973, 596053, 610331, 
...

I've put up a ListPlot of the first sequence (10000 points) here:

http://odo.ca/~haha/j/num/tracks.jpg