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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.)