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URL: https://oeis.org/A051694

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A051694
Smallest Fibonacci number that is divisible by n-th prime.
12
2, 3, 5, 21, 55, 13, 34, 2584, 46368, 377, 832040, 4181, 6765, 701408733, 987, 196418, 591286729879, 610, 72723460248141, 190392490709135, 24157817, 8944394323791464, 160500643816367088, 89, 7778742049, 12586269025
OFFSET
1,1
COMMENTS
It is conjectured that a(n) is not divisible by prime(n)^2. See Remark on p. 528 of Wall and Conjectures in CNRS links. - Michel Marcus, Feb 24 2016
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..650 (first 100 terms from Zak Seidov)
Shalom Eliahou, Mystères Arithmétiques de la Suite de Fibonacci, (in French), Images des Mathématiques, CNRS, 2014.
D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, 67 (1960), 525-532.
FORMULA
a(n) = A000045(A001602(n)). - Max Alekseyev, Dec 12 2007
log a(n) << (n log n)^2. - Charles R Greathouse IV, Jul 17 2012
EXAMPLE
55 is first Fibonacci number that is divisible by 11, the 5th prime, so a(5) = 55.
MAPLE
F:= proc(n) option remember; `if`(n<2, n, F(n-1)+F(n-2)) end:
a:= proc(n) option remember; local p, k; p:=ithprime(n);
for k while irem(F(k), p)>0 do od; F(k)
end:
seq(a(n), n=1..30); # Alois P. Heinz, Sep 28 2015
MATHEMATICA
f[n_] := Block[{fib = Fibonacci /@ Range[n^2]}, Reap@ For[k = 1, k <= n, k++, Sow@ SelectFirst[fib, Mod[#, Prime@ k] == 0 &]] // Flatten //
Rest]; f@ 26 (* Michael De Vlieger, Mar 28 2015, Version 10 *)
PROG
(PARI) a(n)=if(n==3, 5, my(p=prime(n)); fordiv(p^2-1, d, if(fibonacci(d)%p==0, return(fibonacci(d))))) \\ Charles R Greathouse IV, Jul 17 2012
CROSSREFS
KEYWORD
nonn,easy
EXTENSIONS
More terms from Jud McCranie
More terms from James Sellers, Dec 08 1999
STATUS
approved