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

1,6

Comments

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

Links

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

Formula

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

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

Example

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

Prog

(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

Crossrefs

Cf. A000045, A002708.

Sequence in context: A318729 A024467 A215489 * A117364 A193615 A300383

Adjacent sequences: A182164 A182165 A182166 * A182168 A182169 A182170

Keyword

nonn

Author

Alex Ratushnyak, Apr 15 2012

Status

approved