A357531 Final value obtained by traveling clockwise around a circular array with positions numbered clockwise from 1 to n. Each move consists of traveling clockwise k places, where k is the position at the beginning of the move. The first move begins at position 1. a(n) is the position at the end of the n-th move.
1, 2, 2, 4, 2, 4, 2, 8, 8, 4, 2, 4, 2, 4, 8, 16, 2, 10, 2, 16, 8, 4, 2, 16, 7, 4, 26, 16, 2, 4, 2, 32, 8, 4, 18, 28, 2, 4, 8, 16, 2, 22, 2, 16, 17, 4, 2, 16, 30, 24, 8, 16, 2, 28, 43, 32, 8, 4, 2, 16, 2, 4, 8, 64, 32, 64, 2, 16, 8, 44, 2, 64, 2, 4, 68, 16, 18, 64, 2, 16, 80, 4, 2, 64, 32, 4, 8, 80
Offset: 1
Examples
For n = 5, with a circular array of positions numbered clockwise from 1 to 5, start at position 1. On move 1, travel 1 unit clockwise, reaching position 2. On move 2, travel 2 units clockwise, reaching position 4. On move 3, travel 4 units clockwise (almost a full circle), reaching position 3. On move 4, travel 3 units clockwise, reaching position 1. On move 5, travel 1 unit clockwise, reaching position 2. Since the final position at the end of the 5th move is 2, a(5) = 2. (See the illustration in the links.)
Links
- Moosa Nasir, Example of a(5) = 2
- Moosa Nasir, a(2^b) = 2^b
Crossrefs
Cf. A358647 (stepping in digits of n).
Equals {A082495} + 1. - Hugo Pfoertner, Nov 30 2022
Programs
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C
int a(int n) { int current = 1; for (int j = 0; j < n; j++) { current += current; if (current > n) { current = current - n; } } return current; } -
PARI
a(n) = lift(Mod(2,n)^n - 1) + 1; \\ Kevin Ryde, Nov 20 2022
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Python
def A357531(n): return m if (m:=pow(2,n,n)) else n # Chai Wah Wu, Dec 01 2022
Formula
a(n) = ((2^n - 1) mod n) + 1 = A082495(n) + 1. - Jon E. Schoenfield, Nov 20 2022
Comments