

A248593


Least positive integer m such that m + n divides F(m), where F(m) is the mth Fibonacci number given by A000045.


2



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

1,1


COMMENTS

Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n*(n1) 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


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..10000
David M. Bloom, Offset Entries, Solution to Problem B830, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 36, No. 1 (1998), pp. 8990.


EXAMPLE

a(1) = 10 since 10 + 1 = 11 divides F(10) = 55.


MATHEMATICA

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}]


CROSSREFS

Cf. A000045, A247937, A247940, A248588, A248590.
Sequence in context: A344103 A181107 A234974 * A038308 A185221 A349845
Adjacent sequences: A248590 A248591 A248592 * A248594 A248595 A248596


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Oct 09 2014


STATUS

approved



