Posted by Anonymous on Friday, March 30, 2012 at 12:23pm.
1 2 5 10 17 26 37 50 65 82
If you subtract 1 from every number is should be obvious.
0 1 4 9 16 25 36 64 81
These are the perfect squares. So the answer is:
n ^ 2 + 1
Next nunbers :
10 ^ 2 + 1 = 100 + 1 =101
11 ^ 2 + 1 = 121 + 1 = 122
13 ^ 2 + 1 = 169 + 1 = 170
14 ^ 2 + 1 = 196 + 1 = 197
15 ^ 2 + 1 = 225 + 1 = 226
1 4 9 16 31 56 92 141 205 286
In the second pattern, the differences are 1,4,9,16,25,36,49,64,81 which are square numbers.
Next nunbers :
286 + 10 ^ 2 = 286 + 100 = 386
386 + 11 ^ 2 = 386 + 121 = 507
507 + 12 ^ 2 = 507 + 144 = 651
651 + 13 ^ 2 = 651 + 169 = 820
820 + 14 ^ 2 = 820 + 196 = 1016
1 3 9 19 33 51 73 99 129 163
2 n ^ 2 + 1
Next numbers:
2 * 10 ^ 2 + 1 = 2 * 100 + 1 = 200 + 1 = 201
2 * 11 ^ 2 + 1 = 2 * 121 + 1 = 242 + 1 = 243
2 * 12 ^ 2 + 1 = 2 * 144 + 1 = 288 + 1 = 289
2 * 13 ^ 2 + 1 = 2 * 169 + 1 = 338 + 1 = 339
2 * 14 ^ 2 + 1 = 2 * 196 + 1 = 392 + 1 = 393
1 4 11 24 43 72 109 152 205 266
The differences are 3,7,13,19,29,37,43,53,61
which are every other prime number
Nex numbers :
266 + 67 = 333
333 + 73 = 406
406 + 83 = 489
489 + 97 = 586
586 + 103 = 689