A248032 Least positive number k such that n + k divides F(n) + F(k), where F(n) denotes the n-th Fibonacci number.

1, 22, 9, 8, 1, 18, 10, 4, 3, 5, 35, 12, 17, 10, 3, 8, 13, 6, 31, 4, 9, 2, 47, 12, 5, 8, 9, 20, 1, 18, 19, 16, 3, 5, 10, 12, 13, 10, 38, 8, 109, 6, 7, 4, 9, 2, 14, 12, 1, 22, 39, 8, 97, 18, 58, 4, 32, 14, 191, 12, 89, 1, 27, 8, 85, 6, 70, 4, 39, 2, 11, 24, 77, 22, 15, 13, 73, 18, 10

Offset: 1

Author

Derek Orr, Sep 29 2014

Keywords

• nonn

Comments

I believe a(n) exists for all n > 0.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A247937.

Programs

PARI

a(n)=m=1;while((fibonacci(n)+fibonacci(m))%(m+n),m++);m
vector(100,n,a(n))

Extensions

Definition clarified by Chai Wah Wu, Jan 02 2018