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

Allan Wechsler acwacw at gmail.com
Thu Oct 19 05:02:42 CEST 2023

```I don't know ... I like this variation, and it's not *identical *to the
sequence Sean Irvine mentions. (It first parts company from A006509 at
A(30) = 57 rather than 275.)

There are two *other* variations on A006509 in OEIS, at least one of which
matches A006509 for longer than this sequence does. And this sequence
always consists of distinct entries, raising the occurrence question Ali

Sean, were you suggesting it is too similar for inclusion? Or just pointing
out the similarity?

On Wed, Oct 18, 2023 at 10:02 PM Ali Sada via SeqFan <seqfan at list.seqfan.eu>
wrote:

>  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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>
>
>
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```