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

W. Edwin Clark wclark at mail.usf.edu
Fri Oct 20 02:29:31 CEST 2023

```I calculated the first 1000 terms and 5 is the smallest positive integer
not appearing. Among the 1000 terms calculated the positive integers not
appearing are:
5,7,9,10,14,17,20,22,27,30,33,36,39,41,42,44,46,47,50,51,54,55,56,58,59,60,64,65,66,68,69,70,72,74,75,79,82,84,86,87,90,95,96,97,98,99

Also in the interval a(100) to a(1000) there are no entries less than 100.

On Wed, Oct 18, 2023 at 6:13 PM 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
>
>
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
```