[seqfan] Is this sequence a permutation of positive integers?
Ali Sada
pemd70 at yahoo.com
Wed Oct 18 16:06:00 CEST 2023
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
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