This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A345377 #11 Jun 23 2021 10:51:03
%S A345377 1,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,
%T A345377 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
%U A345377 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5
%N A345377 Number of terms m <= n, where m is a term in A006190.
%C A345377 Table 1 of Andrica 2021 paper (p. 24) refers to A006190 as the "bronze Fibonacci" numbers.
%H A345377 Michael De Vlieger, <a href="/A345377/b345377.txt">Table of n, a(n) for n = 0..10000</a>
%H A345377 Dorin Andrica, Ovidiu Bagdasar, and George Cătălin Tųrcąs, <a href="https://doi.org/10.2478/auom-2021-0002">On some new results for the generalised Lucas sequences</a>, An. Şt. Univ. Ovidius Constanţa (Romania, 2021) Vol. 29, No. 1, 17-36. See Section 5.3, pp. 33, Table 4.
%e A345377 a(0)=1, since A006190(0) = 0 and A006190(1) = 1.
%e A345377 a(1)=a(2)=2 since 0 and 1 are the terms in A006190 that do not exceed 1 and 2, respectively.
%e A345377 a(k)=3 for 3 <= k <= 9 since the first terms of A006190 are {0, 1, 3, 10}.
%t A345377 Block[{a = 3, b = -1, nn = 105, u, v = {}}, u = {0, 1}; Do[AppendTo[u, Total[{-b, a} u[[-2 ;; -1]]]]; AppendTo[v, Count[u, _?(# <= i &)]], {i, nn}]; {Boole[First[u] <= 0]}~Join~v] (* or *)
%t A345377 Accumulate@ ReplacePart[ConstantArray[0, Last[#]], Map[# -> 1 &, # + 1]] &@ Fibonacci[Range[0, 5], 3] (* _Michael De Vlieger_, Jun 16 2021 *)
%Y A345377 Cf. A006190, A108852 (Fibonacci), A130245 (Lucas), A345378.
%K A345377 nonn,easy
%O A345377 0,2
%A A345377 _Ovidiu Bagdasar_, Jun 16 2021