A345378 Number of terms m <= n, where m is a term in A006497.

0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset

0,4

Comments

Table 1 of Andrica 2021 paper (p. 24), refers to A006497 as "bronze Lucas" 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)=a(1)=0, since the least term in A006497 is 2.
a(2)=1 since A006497(0) = 2 is followed in that sequence by 3.
a(k)=3 for 3 <= k <= 11 since the first terms of A006490 are {0, 2, 3, 11}.

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 *)
{0}~Join~Accumulate@ ReplacePart[ConstantArray[0, Last[#]], Map[# -> 1 &, #]] &@ LucasL[Range[0, 4], 3] (* Michael De Vlieger, Jun 16 2021 *)

Crossrefs

Cf. A006497, A108852 (Fibonacci), A130245 (Lucas), A345377.

Sequence in context: A331003 A086007 A108582 * A071840 A000193 A059939

Adjacent sequences: A345375 A345376 A345377 * A345379 A345380 A345381

Keyword

nonn,easy

Author

Ovidiu Bagdasar, Jun 16 2021

Status

approved