This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A361423 #178 Jul 23 2023 02:08:03 %S A361423 1,3,9,27,75,225,651,1947,5661,15753,44497,128325,357339,1025029, %T A361423 2881677,8152327,22251081,62981541,175699737,491888331,1353494089, %U A361423 3827528649,10655040429,29413393659,80737582089,226955441541,626061311481,1745916338341,4826531920159,13166998285539 %N A361423 Start with natural numbers, for all positive integer periods p sieve out every p-th number p-1 times over. %C A361423 Appears to grow as: a(n) ~ c n^n/(n-1)! where c is approximately 0.56... %C A361423 The terms remaining after the p-th sieve-batch grow on average with slope p^(p-1)/(p-1)!. %H A361423 Bert Dobbelaere, <a href="/A361423/b361423.txt">Table of n, a(n) for n = 1..600</a> %H A361423 Rok Cestnik, <a href="/A361423/a361423.pdf">Sieve visualization</a> %H A361423 <a href="https://oeis.org/index/Si#sieve">Index entries for sequences generated by sieves</a>. %e A361423 Start with naturals: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, ... %e A361423 Sieve out every 1st number 0 times (do nothing) %e A361423 Sieve out every 2nd number 1 times: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, ... %e A361423 Sieve out every 3rd number 2 times: %e A361423 first time: 1, 3, 7, 9, 13, 15, 19, 21, 25, 27, 31, 33, 37, 39, 43, ... %e A361423 second time: 1, 3, 9, 13, 19, 21, 27, 31, 37, 39, 45, 49, 55, 57, 63, ... %e A361423 Sieve out every 4th number 3 times: %e A361423 first time: 1, 3, 9, 19, 21, 27, 37, 39, 45, 55, 57, 63, 73, 75, 81, ... %e A361423 second time: 1, 3, 9, 21, 27, 37, 45, 55, 57, 73, 75, 81, 93, 99, ... %e A361423 third time: 1, 3, 9, 27, 37, 45, 57, 73, 75, 93, 99, 109, 127, 129, ... %e A361423 Sieve out every 5th number 4 times: %e A361423 first time: 1, 3, 9, 27, 45, 57, 73, 75, 99, 109, 127, 129, 153, 165, ... %e A361423 second time: 1, 3, 9, 27, 57, 73, 75, 99, 127, 129, 153, 165, 189, ... %e A361423 third time: 1, 3, 9, 27, 73, 75, 99, 127, 153, 165, 189, 201, 225, ... %e A361423 fourth time: 1, 3, 9, 27, 75, 99, 127, 153, 189, 201, 225, 261, 289, ... %e A361423 Sieve out every 6th number 5 times: %e A361423 ... %o A361423 (Python) %o A361423 def A361423(n): %o A361423 for p in range(n,1,-1): %o A361423 for k in range(p-1): %o A361423 n += (n-1)//(p-1) %o A361423 return n %o A361423 # _Bert Dobbelaere_, Jul 21 2023 %Y A361423 Cf. A000960 (sieve once each). %Y A361423 Cf. A000959, A111039, A007950, A056533, A099267, A003309. %K A361423 nonn %O A361423 1,2 %A A361423 _Rok Cestnik_, Jul 17 2023 %E A361423 More terms from _Bert Dobbelaere_, Jul 21 2023