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A105701 Smallest m such that 0 is at the n-th position of the decimal representation of the m-th Fibonacci number.

%I A105701 #13 Feb 16 2025 08:32:57
%S A105701 0,32,25,21,34,38,61,40,60,51,61,62,64,71,88,84,88,108,103,103,112,
%T A105701 107,129,118,138,129,131,138,148,152,155,164,166,170,176,174,181,185,
%U A105701 204,196,198,206,212,217,217,258,240,242,244,241,248,252,259,277,265,273
%N A105701 Smallest m such that 0 is at the n-th position of the decimal representation of the m-th Fibonacci number.
%C A105701 a(n) = A000045(a(n)).
%H A105701 Robert Israel, <a href="/A105701/b105701.txt">Table of n, a(n) for n = 0..5000</a>
%H A105701 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number</a>
%e A105701 n=3: a(3)=21, A000045(21) = a(3) = 10946 -> 1[0]946;
%e A105701 n=4: a(4)=34, A000045(34) = a(4) = 5702887 -> 57[0]2887.
%p A105701 N:= 100: # for a(0) to a(N)
%p A105701 F[0]:= 0: F[1]:= 1:
%p A105701 V:= Array(0..N):
%p A105701 count:= 1:
%p A105701 for m from 2 while count < N do
%p A105701   F[m]:= F[m-1]+F[m-2];
%p A105701   L:= convert(F[m], base, 10);
%p A105701   M:= select(t -> L[t+1]=0 and V[t]=0, [$0..min(N, nops(L)-1)]);
%p A105701   count:= count + nops(M);
%p A105701   V[M]:= m;
%p A105701 od:
%p A105701 V[0]:= 0:
%p A105701 convert(V, list); # _Robert Israel_, Jun 03 2020
%Y A105701 Cf. A000045, A072354.
%Y A105701 Cf. A105702, A105703, A105704, A105705, A105706, A105707, A105708, A105709.
%K A105701 nonn,base
%O A105701 0,2
%A A105701 _Reinhard Zumkeller_, Apr 18 2005
%E A105701 a(1) corrected by _Robert Israel_, Jun 03 2020