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A335741 Number of Pell numbers (A000129) <= n. 2
1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The sequence is constant on the interval A000129(k) < n <= A000129(k+1).

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.

FORMULA

a(n) = 1+floor(log_alpha(2*sqrt(2)*n+1)), n>=0, where alpha=1+sqrt(2).

EXAMPLE

The Pell numbers A000129 are 0,1,2,5,12,29,70,...

We have a(2)=a(3)=a(4)=3, since there are three Pell numbers less than or equal to 2,3 and 4, respectively.

MATHEMATICA

Block[{a = 2, 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] (* Michael De Vlieger, Jun 11 2021 *)

CROSSREFS

Cf. A108852 (Fibonacci), A130245 (Lucas), A130253 (Jacobsthal).

Sequence in context: A084526 A081288 A130256 * A103586 A194847 A262070

Adjacent sequences:  A335738 A335739 A335740 * A335742 A335743 A335744

KEYWORD

nonn,changed

AUTHOR

Ovidiu Bagdasar, Jun 20 2020

STATUS

approved

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Last modified June 22 10:56 EDT 2021. Contains 345375 sequences. (Running on oeis4.)