A297573 Least positive integer m such that m*n divides F(m+n), where F(k) denotes the k-th Fibonacci number A000045(k).
1, 1, 1, 2, 14170, 6, 1, 136, 207, 28340, 979, 12, 1, 322, 385, 368, 1, 306, 17, 19780, 3, 68, 1, 24, 524975, 58, 2889, 92, 13, 3570, 12749, 736, 7, 2, 165, 612, 1, 34, 633, 13160, 339, 6, 1, 1846, 5355, 2, 1, 336, 8183, 509950, 21, 116, 1, 918, 4895, 184, 51, 26, 10207, 7140
Offset: 1
Keywords
Examples
a(2) = 1 since 1*2 divides F(1+2) = F(3) = 2. a(4) = 2 since 2*4 divides F(2+4) = 8. a(5) = 14170 since 5*14170 = 70850 divides F(5+14170) = F(14175). a(6) = 6 since 6*6 = 36 divides F(6+6) = F(12) = 144.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..1000 (n = 1..120 from Zhi-Wei Sun)
- Zhi-Wei Sun, Introduction to Lucas sequences, a talk give in 2017.
Programs
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Mathematica
Do[m=1; Label[aa]; If[Mod[Fibonacci[m+n], m*n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}] lpi[n_]:=Module[{k=1},While[!Divisible[Fibonacci[k+n],k*n],k++];k]; Array[ lpi,60] (* Harvey P. Dale, May 05 2018 *) -
PARI
a(n) = my(m=1); while(1, if(Mod(fibonacci(m+n), m*n)==0, return(m)); m++) \\ Felix Fröhlich, Jan 01 2018
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