This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A017910 #51 May 19 2024 02:09:23 %S A017910 1,1,2,2,4,5,8,11,16,22,32,45,64,90,128,181,256,362,512,724,1024,1448, %T A017910 2048,2896,4096,5792,8192,11585,16384,23170,32768,46340,65536,92681, %U A017910 131072,185363,262144,370727,524288 %N A017910 Powers of sqrt(2) rounded down. %C A017910 a(n) is the number of positive squares <= 2^n (cf. A136417). - _Hans Havermann_, Apr 05 2008 %C A017910 If expressed to two significant digits, these are the f-stop numbers in photography: 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, ... %C A017910 There are also "half stops" (sqrt(2)^(n/2)) and "third stops" (sqrt(2)^(n/3)): 1, 1.4, 1.6, 1.8, 2.0, 2.2, 2.5, 2.8, 3.2, 3.6, 4, 4.5, 5, 5.7, 6.3, 7.1, 8, 9, 10. %C A017910 a(n) is also the ratio (rounded down) of the curvature of the circle inscribed in the n-th 45-45-90 triangle to that of the circle inscribed in the 1st triangle, with the triangles arranged in a spiral as shown in the illustration in the links section. - _Kival Ngaokrajang_, Aug 28 2013 %C A017910 a(n) is also the total length of Heighway dragon (rounded down) after n-iterations when L(0) = 1. See illustration in links. - _Kival Ngaokrajang_, Dec 15 2013 %H A017910 Vincenzo Librandi, <a href="/A017910/b017910.txt">Table of n, a(n) for n = 0..1000</a> %H A017910 Kival Ngaokrajang, <a href="/A017910/a017910.pdf">Illustration of initial terms</a>. %H A017910 Kival Ngaokrajang, <a href="/A017910/a017910_1.pdf">Illustration of Heighway dragon for n = 0..5</a>. %H A017910 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dragon_curve">Dragon curve</a>. %F A017910 a(n) = A000196(A000079(n)). - _Jason Kimberley_, Oct 28 2016 %F A017910 a(n) = A017912(n)-1 if n is odd. a(n) = A017912(n) = 2^(n/2) if n is even. - _Chai Wah Wu_, Jul 26 2022 %p A017910 A017910 := n->floor(sqrt(2^n)); # _Peter Luschny_, Sep 20 2011 %t A017910 Floor[(Sqrt[2])^Range[0,40]] (* _Vincenzo Librandi_, Nov 20 2011 *) %o A017910 (PARI) a(n)=sqrtint(2^n) \\ _Charles R Greathouse IV_, Sep 22 2011 %o A017910 (Magma) [Floor(Sqrt(2^n)): n in [0..40]]; // _Vincenzo Librandi_, Nov 20 2011 %o A017910 (Magma) [Isqrt(2^n):n in[0..40]]; // _Jason Kimberley_, Oct 25 2016 %o A017910 (Python) %o A017910 from math import isqrt %o A017910 def A017910(n): return isqrt(1<<n) if n&1 else 1<<(n>>1) # _Chai Wah Wu_, Jul 26 2022 %Y A017910 Cf. A136417, A017912. Bisections: A000079, A084188. %Y A017910 Partial sums of A190568. %K A017910 nonn,easy %O A017910 0,3 %A A017910 _N. J. A. Sloane_