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A105717 Smallest Fibonacci number that has 7 in the n-th position of the decimal representation.

%I A105717 #19 Jul 22 2025 06:00:44
%S A105717 377,377,6765,17711,75025,5702887,267914296,2971215073,701408733,
%T A105717 7778742049,27777890035288,27777890035288,17167680177565,
%U A105717 72723460248141,51680708854858323072,37889062373143906,679891637638612258
%N A105717 Smallest Fibonacci number that has 7 in the n-th position of the decimal representation.
%C A105717 a(n) = A000045(A105707(n)).
%C A105717 The n-th position is counted from the right. - _Harvey P. Dale_, Jul 22 2024
%H A105717 Robert Israel, <a href="/A105717/b105717.txt">Table of n, a(n) for n = 0..995</a>
%H A105717 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number</a>
%e A105717 n=3: A105700(3)=22, a(3)=A000045(22)=17711->1[7]711;
%e A105717 n=4: A105700(4)=25, a(4)=A000045(25)=75025->[7]5025.
%p A105717 N:= 100: # for a(0)..a(N)
%p A105717 F[0]:= 0: F[1]:= 1:
%p A105717 W:= Array(0..N):
%p A105717 count:= 0:
%p A105717 for m from 2 while count < N do
%p A105717   F[m]:= F[m-1]+F[m-2];
%p A105717   L:= convert(F[m],base,10);
%p A105717   M:= select(t -> L[t+1]=7 and W[t]=0, [$0..min(N,nops(L)-1)]);
%p A105717   count:= count + nops(M);
%p A105717   W[M]:= F[m]
%p A105717 od:
%p A105717 convert(W,list); # _Robert Israel_, Jun 01 2020
%t A105717 With[{fibs=Fibonacci[Range[150]]},Table[SelectFirst[fibs,NumberDigit[#,n-1]==7&],{n,20}]] (* _Harvey P. Dale_, Jul 22 2024 *)
%Y A105717 Cf. A105711, A072351, A105712, A105713, A105714, A105715, A105716, A105718, A105719.
%K A105717 nonn,base
%O A105717 0,1
%A A105717 _Reinhard Zumkeller_, Apr 18 2005
%E A105717 Definition corrected by _Robert Israel_, Jun 01 2020