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A112371 Numbers n such that the last 9 decimal digits of the n-th Fibonacci number is pandigital 1-9.

%I A112371 #25 Oct 04 2024 16:51:22
%S A112371 541,919,1788,6355,16257,17799,20411,24347,28837,36485,40784,43450,
%T A112371 45136,45196,51973,54453,54833,57128,57969,63692,67188,67952,69931,
%U A112371 74765,76259,78102,78196,78826,81070,81726,87123,87362,91636,91932
%N A112371 Numbers n such that the last 9 decimal digits of the n-th Fibonacci number is pandigital 1-9.
%C A112371 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
%D A112371 Clifford A. Pickover, "Wonders of Numbers".
%H A112371 Norman Morton and Michael Satteson, <a href="/A112371/b112371.txt">Table of n, a(n) for n = 1..10000</a>, (first 150 terms from Norman Morton)
%e A112371 The 541st Fibonacci number is:
%e A112371 51621 23292 73937 94428 28328 17223 02417 68441 62155 65352
%e A112371 08137 22196 49050 89439 99028 11978 84249 30258 98332 77779
%e A112371 69788 39725 641
%e A112371 which is pandigital 1-9 in its last 9 digits.
%p A112371 f:= proc(n) option remember; f(n-1)+f(n-2) mod 10^9 end proc:
%p A112371 f(0):= 0: f(1):= 1:
%p A112371 filter:= n -> convert(convert(f(n),base,10),set)={$1..9};
%p A112371 select(filter, [$1..10^5]); # _Robert Israel_, Jan 18 2015
%o A112371 (J) NB. In J (www.jsoftware.com).
%o A112371 f=: 3 : '{."(1) 1e9&|@(+/\)@|.^:(<y.) 0 1'
%o A112371 I. (<'123456789')= /:~&.> ":&.> f n
%Y A112371 Cf. A000045, A112516.
%K A112371 nonn,base
%O A112371 1,1
%A A112371 _Roger Hui_, Dec 22 2005