A361423 Start with natural numbers, for all positive integer periods p sieve out every p-th number p-1 times over.
1, 3, 9, 27, 75, 225, 651, 1947, 5661, 15753, 44497, 128325, 357339, 1025029, 2881677, 8152327, 22251081, 62981541, 175699737, 491888331, 1353494089, 3827528649, 10655040429, 29413393659, 80737582089, 226955441541, 626061311481, 1745916338341, 4826531920159, 13166998285539
Offset: 1
Keywords
Examples
Start with naturals: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, ... Sieve out every 1st number 0 times (do nothing) Sieve out every 2nd number 1 times: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, ... Sieve out every 3rd number 2 times: first time: 1, 3, 7, 9, 13, 15, 19, 21, 25, 27, 31, 33, 37, 39, 43, ... second time: 1, 3, 9, 13, 19, 21, 27, 31, 37, 39, 45, 49, 55, 57, 63, ... Sieve out every 4th number 3 times: first time: 1, 3, 9, 19, 21, 27, 37, 39, 45, 55, 57, 63, 73, 75, 81, ... second time: 1, 3, 9, 21, 27, 37, 45, 55, 57, 73, 75, 81, 93, 99, ... third time: 1, 3, 9, 27, 37, 45, 57, 73, 75, 93, 99, 109, 127, 129, ... Sieve out every 5th number 4 times: first time: 1, 3, 9, 27, 45, 57, 73, 75, 99, 109, 127, 129, 153, 165, ... second time: 1, 3, 9, 27, 57, 73, 75, 99, 127, 129, 153, 165, 189, ... third time: 1, 3, 9, 27, 73, 75, 99, 127, 153, 165, 189, 201, 225, ... fourth time: 1, 3, 9, 27, 75, 99, 127, 153, 189, 201, 225, 261, 289, ... Sieve out every 6th number 5 times: ...
Links
- Bert Dobbelaere, Table of n, a(n) for n = 1..600
- Rok Cestnik, Sieve visualization
- Index entries for sequences generated by sieves.
Programs
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Python
def A361423(n): for p in range(n,1,-1): for k in range(p-1): n += (n-1)//(p-1) return n # Bert Dobbelaere, Jul 21 2023
Extensions
More terms from Bert Dobbelaere, Jul 21 2023
Comments