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A361423 Start with natural numbers, for all positive integer periods p sieve out every p-th number p-1 times over. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Appears to grow as: a(n) ~ c n^n/(n-1)! where c is approximately 0.56...
The terms remaining after the p-th sieve-batch grow on average with slope p^(p-1)/(p-1)!.
LINKS
Rok Cestnik, Sieve visualization
EXAMPLE
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:
...
PROG
(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
CROSSREFS
Cf. A000960 (sieve once each).
Sequence in context: A289693 A269684 A330079 * A135415 A182897 A228734
KEYWORD
nonn
AUTHOR
Rok Cestnik, Jul 17 2023
EXTENSIONS
More terms from Bert Dobbelaere, Jul 21 2023
STATUS
approved

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Last modified March 1 06:29 EST 2024. Contains 370430 sequences. (Running on oeis4.)