A112516 Numbers k such that the first 9 decimal digits of the k-th Fibonacci number is 1-9 pandigital.

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

Offset

1,1

Links

Table of n, a(n) for n=1..34.

Example

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.

Maple

filter:= n -> convert(convert(combinat:-fibonacci(n), base, 10)[-9..-1], set) = {$1..9}:
select(filter, [$40.. 5 * 10^4]); # Robert Israel, May 31 2015

Mathematica

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 *)

Prog

(J) NB. (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
NB. 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.

Crossrefs

Cf. A000045, A112371.

Sequence in context: A044885 A159581 A145048 * A325065 A045151 A122107

Adjacent sequences: A112513 A112514 A112515 * A112517 A112518 A112519

Keyword

nonn,base

Author

Roger Hui, Dec 22 2005

Extensions

a(31)-a(34) from Robert G. Wilson v, Dec 27 2005

Status

approved