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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 (list; graph; refs; listen; history; text; internal format)
 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 Zak Seidov and 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. Ron Knott, Fibonacci numbers with tables of F(0)-F(500) 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 Cf. A000045, A001602, A001605, A005478. Sequence in context: A058959 A065398 A084838 * A113650 A259376 A060321 Adjacent sequences:  A051691 A051692 A051693 * A051695 A051696 A051697 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Jud McCranie More terms from James A. Sellers, Dec 08 1999 STATUS approved

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Last modified August 18 10:21 EDT 2022. Contains 356211 sequences. (Running on oeis4.)