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

[Ali Sada]

 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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