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A105708 Smallest m such that 8 is at the n-th position of the decimal representation of the m-th Fibonacci number.

%I A105708 #9 Feb 16 2025 08:32:57
%S A105708 6,11,28,23,38,30,49,50,46,60,54,83,71,81,73,78,90,90,99,97,126,114,
%T A105708 113,135,121,146,136,145,140,145,154,157,170,164,178,186,180,190,188,
%U A105708 203,200,211,207,215,221,246,235,231,242,249,247,272,255,269,267,290,274
%N A105708 Smallest m such that 8 is at the n-th position of the decimal representation of the m-th Fibonacci number.
%C A105708 A105718(n) = A000045(a(n)).
%H A105708 Robert Israel, <a href="/A105708/b105708.txt">Table of n, a(n) for n = 0..5000</a>
%H A105708 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number</a>
%e A105708 n=3: a(3)=23, A000045(23)=A105718(3)=28657->2[8]657;
%e A105708 n=4: a(4)=38, A000045(38)=A105718(4)=39088169->390[8]8169.
%p A105708 N:= 100: # for a(0)..a(N)
%p A105708 V:= Array(0..N): count:= 0:
%p A105708 for m from 1 while count < N+1 do
%p A105708   v:= combinat:-fibonacci(m);
%p A105708   L:= convert(v,base,10);
%p A105708   S:= map(t -> t-1, select(t -> L[t]=8, [$1..nops(L)]));
%p A105708   for s in S do if s <= N and V[s] = 0 then count:= count+1; V[s]:= m fi
%p A105708 od od:
%p A105708 convert(V,list); # _Robert Israel_, Apr 25 2021
%Y A105708 Cf. A105701, A072354, A105702, A105703, A105704, A105705, A105706, A105707, A105709.
%K A105708 nonn,base
%O A105708 0,1
%A A105708 _Reinhard Zumkeller_, Apr 18 2005