A345377 Number of terms m <= n, where m is a term in A006190.

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, 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, 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

Offset

0,2

Comments

Table 1 of Andrica 2021 paper (p. 24) refers to A006190 as the "bronze Fibonacci" numbers.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Dorin Andrica, Ovidiu Bagdasar, and George Cătălin Tųrcąs, On some new results for the generalised Lucas sequences, An. Şt. Univ. Ovidius Constanţa (Romania, 2021) Vol. 29, No. 1, 17-36. See Section 5.3, pp. 33, Table 4.

Example

a(0)=1, since A006190(0) = 0 and A006190(1) = 1.
a(1)=a(2)=2 since 0 and 1 are the terms in A006190 that do not exceed 1 and 2, respectively.
a(k)=3 for 3 <= k <= 9 since the first terms of A006190 are {0, 1, 3, 10}.

Mathematica

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 *)
Accumulate@ ReplacePart[ConstantArray[0, Last[#]], Map[# -> 1 &, # + 1]] &@ Fibonacci[Range[0, 5], 3] (* Michael De Vlieger, Jun 16 2021 *)

Crossrefs

Cf. A006190, A108852 (Fibonacci), A130245 (Lucas), A345378.

Sequence in context: A131981 A257244 A130147 * A096143 A025792 A119447

Adjacent sequences: A345374 A345375 A345376 * A345378 A345379 A345380

Keyword

nonn,easy

Author

Ovidiu Bagdasar, Jun 16 2021

Status

approved