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

Fri Oct 20 04:07:19 CEST 2023

``` Thanks to Allan'sencouragement, as always, I added the sequence to the OEIS. It's now A364054. Ihave put A006509 and A125717 as Cf. based on Fred's and Hugo's excellentobservations. I also added a couple of comments from W. Edwin Clark's email.
Best,

Ali

On Thursday, October 19, 2023 at 08:29:59 PM EDT, W. Edwin Clark <wclark at mail.usf.edu> wrote:

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

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