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A112371 Numbers n such that the last 9 decimal digits of the n-th Fibonacci number is pandigital 1-9. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

REFERENCES

Clifford A. Pickover, "Wonders of Numbers".

LINKS

Norman Morton and Michael Satteson, Table of n, a(n) for n = 1..10000, (first 150 terms from Norman Morton)

EXAMPLE

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.

MAPLE

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};

select(filter, [$1..10^5]); # Robert Israel, Jan 18 2015

PROG

In J (www.jsoftware.com):

f=: 3 : '{."(1) 1e9&|@(+/\)@|.^:(<y.) 0 1'

I. (<'123456789')= /:~&.> ":&.> f n

CROSSREFS

Cf. A000045, A112516.

Sequence in context: A142737 A020378 A160200 * A031937 A031921 A129932

Adjacent sequences:  A112368 A112369 A112370 * A112372 A112373 A112374

KEYWORD

nonn,base

AUTHOR

Roger Hui, Dec 22 2005

STATUS

approved

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Last modified April 23 02:15 EDT 2019. Contains 322380 sequences. (Running on oeis4.)