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A248593
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Least positive integer m such that m + n divides F(m), where F(m) is the m-th Fibonacci number given by A000045.
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2
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10, 6, 84, 12, 16, 7, 27, 9, 144, 30, 28, 12, 8, 30, 14, 18, 57, 19, 342, 18, 20, 24, 66, 12, 9, 27, 144, 60, 112, 35, 16, 24, 60, 55, 20, 12, 40, 111, 24, 36, 88, 72, 80, 48, 10, 15, 72, 24, 224, 18, 50, 54, 270, 72, 54, 33, 224, 18, 28, 12
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OFFSET
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1,1
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COMMENTS
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Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n*(n-1) except for n = 1, 2, 3, 9.
In contrast, it is easy to show that for any integer n > 0, there is a positive integer m such that m + n divides 2^m - 1.
a(n) exists for any n > 0. See Bloom (1998). - Amiram Eldar, Jan 15 2022
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LINKS
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Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
David M. Bloom, Offset Entries, Solution to Problem B-830, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 36, No. 1 (1998), pp. 89-90.
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EXAMPLE
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a(1) = 10 since 10 + 1 = 11 divides F(10) = 55.
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MATHEMATICA
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Do[m=1; Label[aa]; If[Mod[Fibonacci[m], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]
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CROSSREFS
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Cf. A000045, A247937, A247940, A248588, A248590.
Sequence in context: A344103 A181107 A234974 * A038308 A185221 A349845
Adjacent sequences: A248590 A248591 A248592 * A248594 A248595 A248596
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KEYWORD
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nonn
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AUTHOR
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Zhi-Wei Sun, Oct 09 2014
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STATUS
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approved
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