

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
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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, 1736.


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



