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 A084188 a(0)=1, a(n+1) = 2*a(n) + b(n+2), where b(n)=A004539(n) is the n-th bit in the binary expansion of sqrt(2). 4
 1, 2, 5, 11, 22, 45, 90, 181, 362, 724, 1448, 2896, 5792, 11585, 23170, 46340, 92681, 185363, 370727, 741455, 1482910, 2965820, 5931641, 11863283, 23726566, 47453132, 94906265, 189812531, 379625062, 759250124 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Numerators in approximation sqrt(2) ~ a(n)/2^n. a(n) is the number k such that {log_2(k} < 1/2 < {log_2(k+1)}, where { } = fractional part. Equivalently, the jump sequence of f(x) = log_2(x), in the sense that these are the positive integers k for which round(log_2(k)) < round(log_2(k+1)); see A219085. - Clark Kimberling, Jan 01 2013 Largest k such that k^2 <= 2^(2n + 1). - Irina Gerasimova, Jul 07 2013 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 FORMULA a(n) = floor(sqrt(2)*2^n). a(n) = A017910(2*n+1). - # Peter Luschny, Sep 20 2011 MAPLE A084188 := n->floor(sqrt(2)*2^n); # Peter Luschny, Sep 20 2011 MATHEMATICA Table[Floor[Sqrt[2] 2^n], {n, 0, 30}] (* Harvey P. Dale, Aug 15 2013 *) PROG (PARI) a(n)=floor(sqrt(2)< 2 * u + v) a004539_list -- Reinhard Zumkeller, Dec 16 2013 (Magma) [Isqrt(2^(2*n+1)):n in[0..40]] // Jason Kimberley, Oct 25 2016 (PARI) {a(n) = sqrtint(2*4^n)}; /* Michael Somos, Oct 29 2016 */ CROSSREFS Cf. A084185, A084186, A017910. Sequence in context: A071015 A293362 A362583 * A266721 A044432 A033120 Adjacent sequences: A084185 A084186 A084187 * A084189 A084190 A084191 KEYWORD nonn,easy AUTHOR Ralf Stephan, May 18 2003 STATUS approved

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)