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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

N. J. A. Sloane

EXTENSIONS

More terms from Jud McCranie

More terms from James A. Sellers, Dec 08 1999

STATUS

approved

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Last modified September 25 12:56 EDT 2017. Contains 292469 sequences.