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A248032 Least positive number k such that n + k divides F(n) + F(k), where F(n) denotes the n-th Fibonacci number. 3

%I

%S 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,

%T 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,

%U 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

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

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

%H Chai Wah Wu, <a href="/A248032/b248032.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI)

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

%o vector(100,n,a(n))

%Y Cf. A000045, A247937.

%K nonn

%O 1,2

%A _Derek Orr_, Sep 29 2014

%E Definition clarified by _Chai Wah Wu_, Jan 02 2018

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Last modified October 21 05:28 EDT 2021. Contains 348141 sequences. (Running on oeis4.)