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

[Allan Wechsler]

It seems to me that there's enough interest in this variant that Ali Sada
should submit it, of course with cross-references to the other clearly
related sequences (sequences which preserve the remainder mod p(n) at the
n-th step, that is).

On Thu, Oct 19, 2023 at 6:43 PM <hv at crypt.org> wrote:

> Note that A125717 is also relevantly related to Ali Sada's proposed
> sequence, which is then but a step away from Recaman's sequence.
>
> Hugo
>
> Allan Wechsler <acwacw at gmail.com> wrote:
> :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
> :Sada asks.
> :
> :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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> :
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