A182167 Min( f(n), n-f(n) ), where f(n) = A002708(n) = Fibonacci(n) mod n.

0, 1, 1, 1, 0, 2, 1, 3, 2, 5, 1, 0, 1, 1, 5, 5, 1, 8, 1, 5, 5, 1, 1, 0, 0, 1, 7, 11, 1, 10, 1, 5, 13, 1, 5, 0, 1, 1, 2, 5, 1, 8, 1, 19, 20, 1, 1, 0, 13, 25, 19, 23, 1, 8, 5, 21, 17, 1, 1, 0, 1, 1, 20, 5, 5, 14, 1, 3, 25, 15, 1, 0, 1, 1, 25, 3, 2, 34, 1, 5, 7

Offset: 1

Author

Alex Ratushnyak, Apr 15 2012

Keywords

• nonn

Comments

Conjecture: the most frequent values are 0,1,2,3,5,8,13,21,34,... i.e Fibonacci numbers.

Examples

			a(1) = min( A002708(1) , 1 - A002708(1) ) = min(0,1) = 0,  a(4) = min(3,1) = 1,  a(5) = min(0,5) = 0
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A002708.

Programs

PARI

a(n)=my(f=lift(((Mod([1,1;1,0],n))^n)[1,2]));min(f,n-f) \\ Charles R Greathouse IV, Apr 16 2012

Formula

a(n) = min( A002708(n) , n - A002708(n) )

a(n) = min( Fibonacci(n) mod n , n - (Fibonacci(n) mod n) )