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 A247940 Least integer m > n such that m + n divides L(m) + L(n), where L(k) refers to the Lucas number A000032(k). 11
 5, 5, 15, 5, 19, 30, 17, 19, 15, 13, 13, 24, 35, 236, 33, 34, 31, 90, 29, 23, 27, 25, 25, 84, 47, 80, 45, 190, 43, 54, 41, 35, 39, 1216, 37, 72, 59, 212, 57, 43, 55, 66, 53, 86, 51, 76, 49, 60, 71, 53, 69, 55, 67, 222, 65, 122, 63, 112, 61, 264 (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 v(0) = 2, v(1) = A, and v(n+1) = A*v(n) + v(n-1) for n > 0. Then, for any integer n > 0, there are infinitely many positive integers m such that m + n divides v(m) + v(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(3) = 15 since 15 + 3 = 18 divides L(15) + L(3) = 1364 + 4 = 18*76. MATHEMATICA Do[m=n+1; Label[aa]; If[Mod[LucasL[m]+LucasL[n], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}] CROSSREFS Cf. A000032, A247824, A247937. Sequence in context: A294750 A304300 A321653 * A061200 A255304 A330567 Adjacent sequences:  A247937 A247938 A247939 * A247941 A247942 A247943 KEYWORD nonn AUTHOR Zhi-Wei Sun, Sep 27 2014 STATUS approved

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)