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 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 (list; graph; refs; listen; history; text; internal format)
 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(n-1) 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 Zhi-Wei 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 Zhi-Wei Sun, Sep 27 2014 STATUS approved

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Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)