A366494 a(n) is the number of cycles of the map f(x) = 10*x mod (10*n - 1).
8, 1, 1, 8, 2, 1, 5, 6, 2, 53, 1, 4, 8, 3, 1, 14, 4, 1, 41, 2, 16, 29, 1, 34, 8, 49, 1, 26, 2, 7, 11, 16, 4, 5, 3, 2, 80, 1, 1, 26, 2, 1, 83, 2, 14, 29, 9, 2, 8, 1, 1, 14, 2, 27, 17, 16, 2, 5, 9, 2, 14, 1, 25, 26, 16, 1, 5, 8, 14, 5, 1, 2, 32, 3, 5, 50, 4, 17, 5, 4, 4, 143
Offset: 1
Keywords
Examples
For a(4) the 8 cycles are: (1 10 22 25 16 4) (2 20 5 11 32 8) (3 30 27 36 9 12) (6 21 15 33 18 24) (7 31 37 19 34 28) (13) (14 23 35 38 29 17) (26)
Links
- Hillel Wayne, Table of n, a(n) for n = 1..1002
- George Marsaglia, Random Number Generators, Journal of Modern Applied Statistical Methods, Volume 2, Issue 1 (2003).
- Kenneth Shum, Cyclotomic cosets.
Programs
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PARI
a(n)=sumdiv(10*n-1, d, eulerphi(d)/znorder(Mod(10, d)))-1; vector(100, n, a(n-1)) \\ Joerg Arndt, Jan 22 2024
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Python
def get_num_orbits(n: int) -> int: orbits = 0 mod = 10*n - 1 seen = set() for i in range(1, mod): if i not in seen: seen.add(i) orbits += 1 x = 10*i % mod while x != i: seen.add(x) x = 10*x % mod return orbits -
Python
from sympy import totient, n_order, divisors def A366494(n): return sum(totient(d)//n_order(10,d) for d in divisors(10*n-1,generator=True) if d>1) # Chai Wah Wu, Apr 09 2024
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