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A112516
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Numbers n such that the first 9 decimal digits of the n-th Fibonacci number is 1-9 pandigital.
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4
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2749, 4589, 7102, 7727, 8198, 9383, 12633, 15708, 19014, 21206, 21303, 21434, 21566, 22706, 22890, 25790, 28244, 29877, 32174, 32717, 34433, 34883, 37965, 44691, 47422, 48635, 54473, 60438, 60536, 63902, 68340, 72424, 73147, 75873
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internal format)
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OFFSET
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1,1
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LINKS
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EXAMPLE
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The 2749th Fibonacci number is:
14372 68955 33879 17661 82964 56715 64334 14434 76345 06448 91772 ...
which is 1-9 pandigital in its first 9 digits.
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MAPLE
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filter:= n -> convert(convert(combinat:-fibonacci(n), base, 10)[-9..-1], set) = {$1..9}:
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MATHEMATICA
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fQ[n_] := Sort@Take[IntegerDigits@Fibonacci@n, 9] == {1, 2, 3, 4, 5, 6, 7, 8, 9}; Select[ Range[40, 77705], fQ[ # ] &] (* Robert G. Wilson v, Dec 27 2005 *)
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PROG
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In J (www.jsoftware.com):
plus=: 4 : 0
'x xe'=. +. x.
'y ye'=. +. y.
e=. xe>.ye
z=. (x*10^xe-e)+y*10^ye-e
(z%10^b) j. e+b=. 10<:z
)
g =: 3 : '{."1 ({:, plus/)^:(<y.) 0 1'
gi=: 3 : 'I. ''.123456789'' -:"1 /:~"1 ] 10{."1 ] 0j18":, .g y.'
gi n
Basically, using the Fibonacci recurrence using IEEE floating point numbers separately for the mantissa and the exponent, then look for numbers that whose first 9 digits are 1-9 pandigital.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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