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

%I A112516 #19 Apr 21 2024 19:20:03
%S A112516 2749,4589,7102,7727,8198,9383,12633,15708,19014,21206,21303,21434,
%T A112516 21566,22706,22890,25790,28244,29877,32174,32717,34433,34883,37965,
%U A112516 44691,47422,48635,54473,60438,60536,63902,68340,72424,73147,75873
%N A112516 Numbers k such that the first 9 decimal digits of the k-th Fibonacci number is 1-9 pandigital.
%e A112516 The 2749th Fibonacci number is:
%e A112516 14372 68955 33879 17661 82964 56715 64334 14434 76345 06448 91772 ...
%e A112516 which is 1-9 pandigital in its first 9 digits.
%p A112516 filter:= n -> convert(convert(combinat:-fibonacci(n),base,10)[-9..-1],set) = {$1..9}:
%p A112516 select(filter, [$40.. 5 * 10^4]); # _Robert Israel_, May 31 2015
%t A112516 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 *)
%o A112516 (J) NB. (www.jsoftware.com):
%o A112516 plus=: 4 : 0
%o A112516 'x xe'=. +. x.
%o A112516 'y ye'=. +. y.
%o A112516 e=. xe>.ye
%o A112516 z=. (x*10^xe-e)+y*10^ye-e
%o A112516 (z%10^b) j. e+b=. 10<:z
%o A112516 )
%o A112516 g =: 3 : '{."1 ({:,plus/)^:(<y.) 0 1'
%o A112516 gi=: 3 : 'I. ''.123456789'' -:"1 /:~"1 ] 10{."1 ] 0j18":,.g y.'
%o A112516 gi n
%o A112516 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.
%Y A112516 Cf. A000045, A112371.
%K A112516 nonn,base
%O A112516 1,1
%A A112516 _Roger Hui_, Dec 22 2005
%E A112516 a(31)-a(34) from _Robert G. Wilson v_, Dec 27 2005