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A051694
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Smallest Fibonacci number that is divisible by n-th prime.
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12
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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55 is first Fibonacci number that is divisible by 11, the 5th prime, so a(5) = 55.
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MAPLE
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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:
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MATHEMATICA
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f[n_] := Block[{fib = Fibonacci /@ Range[n^2]}, Reap@ For[k = 1, k <= n, k++, Sow@ SelectFirst[fib, Mod[#, Prime@ k] == 0 &]] // Flatten //
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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