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

Thu Oct 19 02:49:59 CEST 2023

``` Well, I can see some similarities here and there, to be honest.Anyway, do you any any organization that gives prizes to people who reinvent the wheel?
Best,
Ali

On Wednesday, October 18, 2023 at 06:18:54 PM EDT, Sean A. Irvine <sairvin at gmail.com> wrote:

Seems very similar to A006509.
https://oeis.org/A006509

On Thu, 19 Oct 2023 at 11:13, Ali Sada via SeqFan <seqfan at list.seqfan.eu> wrote:

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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