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

Author

Moosa Nasir, Nov 19 2022

Keywords

• nonn
• easy

Comments

This is only an empirical observation, but when we graph this sequence, a point always exists at the intersection of y = 2^b and y = -x + 2^(b+1), where b is any integer greater than or equal to 1. This means that a(2^b) = 2^b. This is shown in a link.

Many of the terms seem to be of the form 2^b.

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. A015910, A082495.

Cf. A358647 (stepping in digits of n).

Equals {A082495} + 1. - Hugo Pfoertner, Nov 30 2022

Programs

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

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