At 06:25 PM 2/13/04, Richard Guy wrote:
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 ... R.
That 20 should be a 16 (corresponding to the prime 373). Here are the first 100 terms of both sequences: 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. 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. Every positive integer up to 82 appears in the first 100 terms; everything up to 922 appears in the first 1000. Note that, apart from a(1), odd-index terms must be even; even-index terms are occasionally even as well, so the odd values tend to arrive late.
On Fri, 13 Feb 2004, Leroy Quet wrote:
Let a(1) = 1;
Let a(m) be the lowest yet unpicked positive integer such that:
sum{k=1 to m} k* a(k)
is a prime.
-- Fred W. Helenius <fredh@ix.netcom.com>