A357531 - OEIS

%I #68 Apr 27 2024 09:37:44

%S 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,

%T 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,

%U 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

%N 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.

%C 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.

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

%H Moosa Nasir, <a href="https://raw.githubusercontent.com/TealEgg/MoosaNasir/main/Examplen5v2.png">Example of a(5) = 2</a>

%H Moosa Nasir, <a href="https://raw.githubusercontent.com/TealEgg/MoosaNasir/main/Intersections.png">a(2^b) = 2^b</a>

%F a(n) = ((2^n - 1) mod n) + 1 = A082495(n) + 1. - _Jon E. Schoenfield_, Nov 20 2022

%e For n = 5, with a circular array of positions numbered clockwise from 1 to 5, start at position 1.

%e On move 1, travel 1 unit clockwise, reaching position 2.

%e On move 2, travel 2 units clockwise, reaching position 4.

%e On move 3, travel 4 units clockwise (almost a full circle), reaching position 3.

%e On move 4, travel 3 units clockwise, reaching position 1.

%e On move 5, travel 1 unit clockwise, reaching position 2.

%e Since the final position at the end of the 5th move is 2, a(5) = 2. (See the illustration in the links.)

%o (C)

%o int a(int n)

%o {

%o     int current = 1;

%o     for (int j = 0; j < n; j++) {

%o         current += current;

%o         if (current > n) {

%o             current = current - n;

%o         }

%o     }

%o     return current;

%o }

%o (PARI) a(n) = lift(Mod(2,n)^n - 1) + 1; \\ _Kevin Ryde_, Nov 20 2022

%o (Python)

%o def A357531(n): return m if (m:=pow(2,n,n)) else n # _Chai Wah Wu_, Dec 01 2022

%Y Cf. A015910, A082495.

%Y Cf. A358647 (stepping in digits of n).

%Y Equals {A082495} + 1. - _Hugo Pfoertner_, Nov 30 2022

%K nonn,easy

%O 1,2

%A _Moosa Nasir_, Nov 19 2022