

A247937


Least integer m > n such that m + n divides F(m) + F(n), where F(k) refers to the Fibonacci number A000045(k).


16



5, 22, 9, 8, 8, 18, 10, 16, 21, 14, 35, 24, 17, 34, 21, 32, 20, 30, 31, 28, 87, 26, 47, 36, 28, 46, 63, 32, 80, 42, 151, 40, 75, 38, 38, 60, 113, 39, 51, 56, 109, 49, 307, 52, 63, 50, 50, 72, 101, 70, 57, 68, 97, 66, 58, 64, 93, 62, 191, 84
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OFFSET

1,1


COMMENTS

Conjecture: Let A be any integer not congruent to 3 modulo 6. Define u(0) = 0, u(1) = 1, and u(n+1) = A*u(n) + u(n1) for n > 0. Then, for any integer n > 0, there are infinitely many positive integers m such that m + n divides u(m) + u(n).
This implies that a(n) exists for any n > 0.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..10000


EXAMPLE

a(2) = 22 since 22 + 2 = 24 divides F(22) + F(2) = 17711 + 1 = 17712 = 24*738.


MATHEMATICA

Do[m=n+1; Label[aa]; If[Mod[Fibonacci[m]+Fibonacci[n], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]


CROSSREFS

Cf. A000045, A247824, A247940, A248032.
Sequence in context: A220002 A156860 A225846 * A343840 A270406 A209049
Adjacent sequences: A247934 A247935 A247936 * A247938 A247939 A247940


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Sep 27 2014


STATUS

approved



