A345379 Number of terms m <= n, where m is a term in the bisection of Lucas numbers (A005248).

0, 0, 1, 2, 2, 2, 2, 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, 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

0,4

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 5.4, pp. 33-34, Table 4.

Example

a(0)=a(1)=0, since the least term in A005248 is 2.
a(2)=1 since A005248(0) = 2 is followed in that sequence by 3.
a(k)=3 for 3 <= k <= 6 since the first terms of A005248 are {0, 2, 3, 7}.

Mathematica

Block[{a = 3, b = 1, nn = 105, u, v = {}}, u = {2, a}; 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, 10, 2] (* Michael De Vlieger, Jun 16 2021 *)

Crossrefs

Cf. A005248, A108852 (Fibonacci), A130245 (Lucas), A130260.

Sequence in context: A163291 A156875 A066339 * A052375 A212625 A309398

Adjacent sequences: A345376 A345377 A345378 * A345380 A345381 A345382

Keyword

nonn,easy

Author

Ovidiu Bagdasar, Jun 16 2021

Status

approved