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A112371
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Numbers n such that the last 9 decimal digits of the n-th Fibonacci number is pandigital 1-9.
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5
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541, 919, 1788, 6355, 16257, 17799, 20411, 24347, 28837, 36485, 40784, 43450, 45136, 45196, 51973, 54453, 54833, 57128, 57969, 63692, 67188, 67952, 69931, 74765, 76259, 78102, 78196, 78826, 81070, 81726, 87123, 87362, 91636, 91932
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OFFSET
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1,1
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COMMENTS
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Since the Fibonacci sequence mod 10^9 is periodic with period 1500000000, there is some positive M such that this sequence satisfies a(n+M) = a(n) + 1500000000. - Robert Israel, Jan 18 2015
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REFERENCES
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Clifford A. Pickover, "Wonders of Numbers".
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LINKS
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EXAMPLE
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The 541st Fibonacci number is:
51621 23292 73937 94428 28328 17223 02417 68441 62155 65352
08137 22196 49050 89439 99028 11978 84249 30258 98332 77779
69788 39725 641
which is pandigital 1-9 in its last 9 digits.
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MAPLE
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f:= proc(n) option remember; f(n-1)+f(n-2) mod 10^9 end proc:
f(0):= 0: f(1):= 1:
filter:= n -> convert(convert(f(n), base, 10), set)={$1..9};
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PROG
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In J (www.jsoftware.com):
f=: 3 : '{."(1) 1e9&|@(+/\)@|.^:(<y.) 0 1'
I. (<'123456789')= /:~&.> ":&.> f n
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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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STATUS
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approved
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