[seqfan] Is this sequence a permutation of positive integers?

[Ali Sada]

Hi everyone,
a(1) = 1, for n > 1, a(n) is the least positive integer, not already in the sequence, that satisfies the following condition: a(n) mod p(n-1) = a(n-1) mod p(n-1).
p(1) = 2, a(1) = 1, a(1) mod 2 =1, so a(2) = 3 because 3 mod 2 =1.p(2) = 3, a(2) mod 3 = 0, and the least positive integer that's mod 3= 0 is 6, so a(3) =6.p(3) =5, a(3) mod (5) =1, so a(4) =11, and so on.
Will all positive integers appear in this sequence? Also, is it good for the OEIS? 



1, 3, 6, 11, 4, 15, 2, 19, 38, 61, 32, 63, 26, 67, 24, 71, 18,77, 16, 83, 12, 85, 164, 81, 170, 73, 174, 277, 384, 57, 283, 29, 160, 23, 162,13, 315, 158, 321, 154, 327, 148, 329, 138, 331, 134, 333, 122, 345, 118, 347, 114,353, 112, 363, 106, 369, 100, 371, 94, 375, 92, 385, 78, 389, 76, 393, 62, 399,52, 401, 48, 407, 40, 413, 34, 417, 28, 425, 826, 8, 427, 848, 1279, 846, 1285,842, 1291, 377, 838, 1301, 367, 1325, 351, 1333, 335, 1341, 323, 844, 1367, 285,832, 275, 1401, 263, 834, 257, 1431, 245, 1443, 241, 1455, 229, 1463, 225, 856,215, 858, 211, 864, 205, 866, 193, 870, 187, 878, 177, 886, 167, 894, 161, 900,157, 908, 151, 912, 143, 916, 129, 926, 117, 928, 107, 930, 103, 932, 93, 946, 89,948, 1811, 934, 53, 936, 49, 956, 45, 964, 35, 972, 31, 978, 25, 992, 21, 998, 1981,990, 1987, 2996, 970, 1989, 968, 1999, 966, 2005, 3054, 952, 2013, 950, 2019, 3106,924, 2017, 920, 2023, 914, 2031, 3154, 896, 2047, 3200, 874, 2045, 3226, 852, 3238,836, 2049, 3266, 820


 
Best,
Ali